OneAwayFromPrime.py

# OneAwayFromPrime.py

# Hypothesis:
#Given any prime p expressed as a+b, there is always a pair a,b
#such that p = a+b, and such that 2^a*3^b is one away from a prime

#The main reason for this script is to test this hypothesis on as many primes as fast as possible.
# It finds the smallest big prime determined by each smaller prime. This is the fastest way to test.
# For speed, for each off_p I test 2**a*3**b from a = 1 and b = off_p - 1. On the other hand, if
# I wanted to find the biggest prime of several determined by each p, I'd test from b = 1 and
# a = off_p - 1. This is because cubes always overpower squares.

import gmpy2
from gmpy2 import is_prime
from math import log10
from time import time, ctime
import winsound

def find_prime_before_n(n):
    for x in range(n, 2, -1):
        if isPrime(x):
            return x

def int_digits(n):
    """
    return number of digits of an integer
    """
    return int(log10(n) + 1)

def sig_digits(n, d=6):
    """
    Return any real number n to d significant digits, in scientific notation.
    """
    return '%.*e' % (d-1, n)

def isPrime(n):
    """
    Return True if n is prime, False if not prime.
    """
    if not isinstance(n, int):
        raise TypeError("The argument to isPrime() must be an int.")
    x = gmpy2.is_prime(n, 25)
    return x != False


def secsToHMS(seconds):
    """
    Convert seconds to hours:minutes:seconds, with seconds rounded to hundredths of a second.
    """
    minutes, seconds = divmod(seconds, 60)
    hours, minutes = divmod(minutes, 60)
    return "%02d:%02d:%05.2f" % (hours, minutes, seconds)

def nextNPrimes(m,n=1):
    """
    Return list of n primes >= m and smaller than any other primes
    """
    count = 0
    primes = []
    if m % 2 == 0:
        m += 1
    while count < n:
        if isPrime(m):
            primes.append(m)
            count += 1
        m += 2
    return primes


def adjusting(z):
    if len(str(z)) > 3 and z >= 100:
        z = int(str(z).split(".")[0])
        return z
    else:
        return z

def density(num_of_primes, last_prime):
    if prime_before_n == n:
        return (num_of_primes)/((last_prime - n) + 1)
    else:
        return (num_of_primes)/(last_prime - prime_before_n + 1)

def prime_to_big_prime(p):
    """
    Given a prime, return a much bigger one.

    For every prime p there there is at least one pair of positive integers a and b such
    that p = a + b, and such that 2**a*3**b is either 1 greater than or 1 less than another
    (much larger) prime. This function returns the pair that produces the smallest value
    of 2**a*3**b, and the smallest of the big primes that p determines. The interest is in
    speed, not size.
    """
    for b in range(1,p):
        a = p - b
        one_off_big_p = 2**a*3**b
        for big_p in [one_off_big_p - 1, one_off_big_p + 1]:
            if isPrime(big_p):
                return big_p, a, b

begin = time()

n = 8831 #  <-- set these
m = 10

primes_list = nextNPrimes(n,m)

last_prime = primes_list[-1]

primes_for_which_condition_holds = []

num_of_primes = len(primes_list)
if num_of_primes <= 100:
    print("These primes will be tested:", primes_list)
else:
    print("The first 10 of the", num_of_primes, "primes to be tested:", primes_list[:10])
    print()
    print("The last 10 of the", num_of_primes, "primes to be tested:", primes_list[-10:])
print("Testing", num_of_primes,  "primes, from", primes_list[0], "to", last_prime,"starting at", ctime()[11:19])

prime_before_n = find_prime_before_n(n)

density = density(num_of_primes, last_prime)
print("density =", round(density,3))



count_failures = 0
failures_list = []
times_list = []
num_digits = 1
max_num_digits = 1
prev_max_num_digits = 1
ra = 0
prev_ra = 0

for i,p in enumerate(primes_list):
    t0 = time()
    big_p, a, b = prime_to_big_prime(p)
    t1 = time()
    num_digits = int_digits(big_p)
    prev_max_num_digits = max_num_digits
    if num_digits > max_num_digits:
        max_num_digits = num_digits
        flag2 = 1
        #print("A big one", num_digits, "digits!")
        #winsound.PlaySound("tada", winsound.SND_ALIAS)
    winsound.PlaySound("/P31Working/Sounds/beat", winsound.SND_ALIAS)
    t = float(sig_digits(t1-t0,3))
    t = adjusting(t)

    times_list.insert(0,t)
    tlnum = len(times_list)
    if tlnum >= 50:
        times_list.pop()
    prev_ra = ra
    #running_avg = float(numberRounding(sum(times_list)/len(times_list),3))
    running_avg = float(sum(times_list)/len(times_list))
    running_avg = adjusting(running_avg)
    ra = running_avg
    print(p," = ",a," + ",b," | ",num_digits," digits (",prev_max_num_digits,") | ", secsToHMS(t)," | running ",tlnum, " avg ",secsToHMS(ra), " | ", ctime()[11:19], " | p ",i+1," of ",num_of_primes, sep="")
    if flag2 == 1 and prev_max_num_digits > 1:
        ratio2 = float(sig_digits(num_digits/prev_max_num_digits,3))
        if ratio2 > 1.1:
            ratio2 = adjusting(ratio2)
            print("A big one!!", num_digits, "digits is", ratio2, "times the previous largest number of digits", prev_max_num_digits)
            winsound.PlaySound("/P31Working/Sounds/beat", winsound.SND_ALIAS)
            print()
    if t > 3*prev_ra and prev_ra != 0:
        ratio = float(sig_digits(t/prev_ra,3))
        ratio = adjusting(ratio)

        print("That was a tough one! The time of", t, "was", ratio, "times that of the previous running avg",prev_ra)
        winsound.PlaySound("/P31Working/Sounds/beat", winsound.SND_ALIAS)
        print()

    prev_ra = ra
    primes_for_which_condition_holds.append(p)




"""
tested evens, 1000 to 2000
There were 57 failures: [1002, 1046, 1050, 1058, 1092, 1122, 1130, 1138, 1150, 1170, 1182,
 1194, 1202, 1262, 1274, 1298, 1302, 1306, 1308, 1320, 1344, 1354, 1406, 1418, 1428, 1446,
1454, 1458, 1478, 1506, 1514, 1542, 1566, 1578, 1606, 1608, 1618, 1622, 1650, 1666, 1718,
1770, 1802, 1822, 1826, 1850, 1854, 1858, 1862, 1906, 1918, 1922, 1930, 1970, 1974, 1978, 1998]
total time was 3076.823

The first 10 of the 10000 primes to be tested: [5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281]

The last 10 of the 10000 primes to be tested: [112759, 112771, 112787, 112799, 112807, 112831, 112843, 112859, 112877, 112901]
Testing 10000 primes, from 5197 to 112901 starting at 15:58:09
density = 0.093
Good: 5197 = 4167 + 1030 | 1746 digits (1) | Time 434 | running 1 avg 434 | 16:05:23 | p 1 of 10000
Good: 5209 = 2277 + 2932 | 2085 digits (1746) | Time 1450 | running 2 avg 942 | 16:29:35 | p 2 of 10000
A big one!! 2085 digits is 1.19 times the previous largest number of digits 1746

That was a tough one! The time of 1450 was 3.34 times that of the previous running avg 434

Good: 5227 = 5047 + 180 | 1606 digits (2085) | Time 119 | running 3 avg 668 | 16:31:39 | p 3 of 10000
Good: 5231 = 4833 + 398 | 1645 digits (2085) | Time 181 | running 4 avg 546 | 16:34:40 | p 4 of 10000
Good: 5233 = 4460 + 773 | 1712 digits (2085) | Time 346 | running 5 avg 506 | 16:40:26 | p 5 of 10000
Good: 5237 = 4901 + 336 | 1636 digits (2085) | Time 165 | running 6 avg 449 | 16:43:11 | p 6 of 10000
Good: 5261 = 5196 + 65 | 1596 digits (2085) | Time 74.2 | running 7 avg 396 | 16:44:25 | p 7 of 10000
Good: 5273 = 4868 + 405 | 1659 digits (2085) | Time 201 | running 8 avg 371 | 16:47:46 | p 8 of 10000
Good: 5279 = 4753 + 526 | 1682 digits (2085) | Time 233 | running 9 avg 356 | 16:51:39 | p 9 of 10000
Good: 5281 = 5184 + 97 | 1607 digits (2085) | Time 84.3 | running 10 avg 329 | 16:53:04 | p 10 of 10000
Good: 5297 = 4932 + 365 | 1659 digits (2085) | Time 179 | running 11 avg 315 | 16:56:02 | p 11 of 10000
Good: 5303 = 5263 + 40 | 1604 digits (2085) | Time 62.5 | running 12 avg 294 | 16:57:05 | p 12 of 10000
Good: 5309 = 5125 + 184 | 1631 digits (2085) | Time 111 | running 13 avg 280 | 16:58:56 | p 13 of 10000
Good: 5323 = 5155 + 168 | 1632 digits (2085) | Time 118 | running 14 avg 268 | 17:00:54 | p 14 of 10000
Good: 5333 = 5156 + 177 | 1637 digits (2085) | Time 108 | running 15 avg 258 | 17:02:43 | p 15 of 10000
Good: 5347 = 4331 + 1016 | 1789 digits (2085) | Time 449 | running 16 avg 270 | 17:10:12 | p 16 of 10000
Good: 5351 = 5120 + 231 | 1652 digits (2085) | Time 136 | running 17 avg 262 | 17:12:28 | p 17 of 10000
Good: 5381 = 5163 + 218 | 1659 digits (2085) | Time 130 | running 18 avg 254 | 17:14:37 | p 18 of 10000
Good: 5387 = 5301 + 86 | 1637 digits (2085) | Time 88.5 | running 19 avg 246 | 17:16:06 | p 19 of 10000
Good: 5393 = 4896 + 497 | 1711 digits (2085) | Time 243 | running 20 avg 246 | 17:20:09 | p 20 of 10000
Good: 5399 = 5249 + 150 | 1652 digits (2085) | Time 111 | running 21 avg 239 | 17:22:00 | p 21 of 10000
Good: 5407 = 5281 + 126 | 1650 digits (2085) | Time 95.7 | running 22 avg 233 | 17:23:36 | p 22 of 10000
Good: 5413 = 5255 + 158 | 1658 digits (2085) | Time 110 | running 23 avg 227 | 17:25:26 | p 23 of 10000
Good: 5417 = 4911 + 506 | 1720 digits (2085) | Time 241 | running 24 avg 228 | 17:29:27 | p 24 of 10000
Good: 5419 = 4072 + 1347 | 1869 digits (2085) | Time 635 | running 25 avg 244 | 17:40:02 | p 25 of 10000
That was a tough one! The time of 635 was 2.79 times that of the previous running avg 228

Testing 100 primes, from 5693 to 6569 starting at 03:19:10
density = 0.114
Good: 5693 = 5562 + 131 | 1737 digits (1) | Time 113 | running 1 avg 113 | 03:21:04 | p 1 of 100
Good: 5701 = 5491 + 210 | 1754 digits (1737) | Time 146 | running 2 avg 130 | 03:23:30 | p 2 of 100
Good: 5711 = 5585 + 126 | 1742 digits (1754) | Time 125 | running 3 avg 128 | 03:25:35 | p 3 of 100
Good: 5717 = 5221 + 496 | 1809 digits (1754) | Time 301 | running 4 avg 171 | 03:30:36 | p 4 of 100
That was a tough one! The time of 301 was 2.35 times that of the previous running avg 128

Good: 5737 = 5562 + 175 | 1758 digits (1809) | Time 156 | running 5 avg 168 | 03:33:15 | p 5 of 100
Good: 5741 = 5118 + 623 | 1838 digits (1809) | Time 349 | running 6 avg 198 | 03:39:04 | p 6 of 100
That was a tough one! The time of 349 was 2.08 times that of the previous running avg 168

Good: 5743 = 5452 + 291 | 1781 digits (1838) | Time 182 | running 7 avg 196 | 03:42:10 | p 7 of 100
Good: 5749 = 5619 + 130 | 1754 digits (1838) | Time 126 | running 8 avg 187 | 03:44:15 | p 8 of 100
Good: 5779 = 5750 + 29 | 1745 digits (1838) | Time 83.9 | running 9 avg 176 | 03:45:39 | p 9 of 100
Good: 5783 = 5339 + 444 | 1820 digits (1838) | Time 260 | running 10 avg 184 | 03:49:59 | p 10 of 100
Good: 5791 = 5535 + 256 | 1789 digits (1838) | Time 184 | running 11 avg 184 | 03:53:03 | p 11 of 100
Good: 5801 = 5348 + 453 | 1827 digits (1838) | Time 264 | running 12 avg 191 | 03:57:28 | p 12 of 100
Good: 5807 = 5070 + 737 | 1878 digits (1838) | Time 404 | running 13 avg 207 | 04:04:12 | p 13 of 100
That was a tough one! The time of 404 was 2.12 times that of the previous running avg 191

Good: 5813 = 5658 + 155 | 1778 digits (1878) | Time 135 | running 14 avg 202 | 04:06:30 | p 14 of 100
Good: 5821 = 5776 + 45 | 1761 digits (1878) | Time 90.1 | running 15 avg 195 | 04:08:00 | p 15 of 100
Good: 5827 = 5804 + 23 | 1759 digits (1878) | Time 86.5 | running 16 avg 188 | 04:09:26 | p 16 of 100
Good: 5839 = 5573 + 266 | 1805 digits (1878) | Time 177 | running 17 avg 187 | 04:12:23 | p 17 of 100
Good: 5843 = 4774 + 1069 | 1948 digits (1878) | Time 597 | running 18 avg 210 | 04:22:21 | p 18 of 100
That was a tough one! The time of 597 was 3.19 times that of the previous running avg 187

Good: 5849 = 5816 + 33 | 1767 digits (1948) | Time 75.8 | running 19 avg 203 | 04:23:39 | p 19 of 100
Good: 5851 = 5091 + 760 | 1896 digits (1948) | Time 417 | running 20 avg 214 | 04:30:37 | p 20 of 100
That was a tough one! The time of 417 was 2.05 times that of the previous running avg 203

Good: 5857 = 5329 + 528 | 1857 digits (1948) | Time 311 | running 21 avg 218 | 04:35:50 | p 21 of 100
Good: 5861 = 5846 + 15 | 1767 digits (1948) | Time 78.4 | running 22 avg 212 | 04:37:09 | p 22 of 100
Good: 5867 = 5474 + 393 | 1836 digits (1948) | Time 247 | running 23 avg 213 | 04:41:16 | p 23 of 100
Good: 5869 = 5614 + 255 | 1812 digits (1948) | Time 187 | running 24 avg 212 | 04:44:24 | p 24 of 100
Good: 5879 = 5284 + 595 | 1875 digits (1948) | Time 341 | running 25 avg 217 | 04:50:05 | p 25 of 100
Good: 5881 = 5030 + 851 | 1921 digits (1948) | Time 463 | running 26 avg 227 | 04:57:48 | p 26 of 100
That was a tough one! The time of 463 was 2.13 times that of the previous running avg 217

Good: 5897 = 5678 + 219 | 1814 digits (1948) | Time 163 | running 27 avg 225 | 05:00:34 | p 27 of 100
Good: 5903 = 5297 + 606 | 1884 digits (1948) | Time 354 | running 28 avg 229 | 05:06:28 | p 28 of 100
Good: 5923 = 4896 + 1027 | 1964 digits (1948) | Time 573 | running 29 avg 241 | 05:16:01 | p 29 of 100
That was a tough one! The time of 573 was 2.5 times that of the previous running avg 229

Good: 5927 = 5839 + 88 | 1800 digits (1964) | Time 106 | running 30 avg 237 | 05:17:50 | p 30 of 100
Good: 5939 = 5801 + 138 | 1813 digits (1964) | Time 144 | running 31 avg 234 | 05:20:14 | p 31 of 100
Good: 5953 = 5938 + 15 | 1795 digits (1964) | Time 74.5 | running 32 avg 229 | 05:21:29 | p 32 of 100
Good: 5981 = 5826 + 155 | 1828 digits (1964) | Time 149 | running 33 avg 226 | 05:23:58 | p 33 of 100
Good: 5987 = 5774 + 213 | 1840 digits (1964) | Time 177 | running 34 avg 225 | 05:26:55 | p 34 of 100
Good: 6007 = 3729 + 2278 | 2210 digits (1964) | Time 1420 | running 35 avg 259 | 05:50:32 | p 35 of 100
A big one!! 2210 digits is 1.13 times the previous largest number of digits 1964

That was a tough one! The time of 1420 was 6.31 times that of the previous running avg 225

Good: 6011 = 4637 + 1374 | 2052 digits (2210) | Time 826 | running 36 avg 275 | 06:04:23 | p 36 of 100
That was a tough one! The time of 826 was 3.19 times that of the previous running avg 259

Good: 6029 = 6024 + 5 | 1816 digits (2210) | Time 81.7 | running 37 avg 269 | 06:05:47 | p 37 of 100
Good: 6037 = 6029 + 8 | 1819 digits (2210) | Time 71.4 | running 38 avg 264 | 06:06:59 | p 38 of 100
Good: 6043 = 5941 + 102 | 1838 digits (2210) | Time 124 | running 39 avg 261 | 06:09:03 | p 39 of 100
Good: 6047 = 5852 + 195 | 1855 digits (2210) | Time 154 | running 40 avg 258 | 06:11:37 | p 40 of 100
Good: 6053 = 5886 + 167 | 1852 digits (2210) | Time 152 | running 41 avg 255 | 06:14:08 | p 41 of 100
Process terminated with an exit code of -2

Testing 100 primes, from 6067 to 6917 starting at 09:45:32
density = 0.116
Good: 6067 = 5245 + 822 | 1972 digits (1) | Time 509 | running 1 avg 509 | 09:54:02 | p 1 of 100
Good: 6073 = 5242 + 831 | 1975 digits (1972) | Time 493 | running 2 avg 501 | 10:02:15 | p 2 of 100
Good: 6079 = 5987 + 92 | 1847 digits (1975) | Time 116 | running 3 avg 373 | 10:04:11 | p 3 of 100
Good: 6089 = 5842 + 247 | 1877 digits (1975) | Time 196 | running 4 avg 328 | 10:07:28 | p 4 of 100
Good: 6091 = 5881 + 210 | 1871 digits (1975) | Time 165 | running 5 avg 296 | 10:10:13 | p 5 of 100
Good: 6101 = 5996 + 105 | 1856 digits (1975) | Time 137 | running 6 avg 269 | 10:12:30 | p 6 of 100
Good: 6113 = 5960 + 153 | 1868 digits (1975) | Time 146 | running 7 avg 252 | 10:14:56 | p 7 of 100
Good: 6121 = 5806 + 315 | 1899 digits (1975) | Time 225 | running 8 avg 248 | 10:18:42 | p 8 of 100
Good: 6131 = 5890 + 241 | 1889 digits (1975) | Time 204 | running 9 avg 243 | 10:22:06 | p 9 of 100
Good: 6133 = 5858 + 275 | 1895 digits (1975) | Time 217 | running 10 avg 241 | 10:25:43 | p 10 of 100
Good: 6143 = 5889 + 254 | 1894 digits (1975) | Time 206 | running 11 avg 238 | 10:29:09 | p 11 of 100
Good: 6151 = 5526 + 625 | 1962 digits (1975) | Time 403 | running 12 avg 251 | 10:35:52 | p 12 of 100
Good: 6163 = 5779 + 384 | 1923 digits (1975) | Time 268 | running 13 avg 253 | 10:40:20 | p 13 of 100
Good: 6173 = 6062 + 111 | 1878 digits (1975) | Time 130 | running 14 avg 244 | 10:42:30 | p 14 of 100
*Good: 6197 = 3282 + 2915 | 2379 digits (1975) | Time 2180 | running 15 avg 373 | 11:18:47 | p 15 of 100
A big one!! 2379 digits is 1.2 times the previous largest number of digits 1975

That was a tough one! The time of 2180 was 8.93 times that of the previous running avg 244

Good: 6199 = 6018 + 181 | 1898 digits (2379) | Time 177 | running 16 avg 361 | 11:21:50 | p 16 of 100
Good: 6203 = 5973 + 230 | 1908 digits (2379) | Time 193 | running 17 avg 351 | 11:25:02 | p 17 of 100
Good: 6211 = 5658 + 553 | 1968 digits (2379) | Time 423 | running 18 avg 355 | 11:32:05 | p 18 of 100
Good: 6217 = 5757 + 460 | 1953 digits (2379) | Time 336 | running 19 avg 354 | 11:37:41 | p 19 of 100
Good: 6221 = 5813 + 408 | 1945 digits (2379) | Time 310 | running 20 avg 352 | 11:42:51 | p 20 of 100
Good: 6229 = 5757 + 472 | 1959 digits (2379) | Time 351 | running 21 avg 352 | 11:48:42 | p 21 of 100
Good: 6247 = 5332 + 915 | 2042 digits (2379) | Time 641 | running 22 avg 365 | 11:59:24 | p 22 of 100
Good: 6257 = 5909 + 348 | 1945 digits (2379) | Time 270 | running 23 avg 361 | 12:03:53 | p 23 of 100
Good: 6263 = 6128 + 135 | 1910 digits (2379) | Time 171 | running 24 avg 353 | 12:06:45 | p 24 of 100
Good: 6269 = 5825 + 444 | 1966 digits (2379) | Time 331 | running 25 avg 352 | 12:12:16 | p 25 of 100
Good: 6271 = 5494 + 777 | 2025 digits (2379) | Time 520 | running 26 avg 358 | 12:20:55 | p 26 of 100
Good: 6277 = 5891 + 386 | 1958 digits (2379) | Time 357 | running 27 avg 358 | 12:26:52 | p 27 of 100
Good: 6287 = 5997 + 290 | 1944 digits (2379) | Time 250 | running 28 avg 354 | 12:31:02 | p 28 of 100
Good: 6299 = 5724 + 575 | 1998 digits (2379) | Time 435 | running 29 avg 357 | 12:38:17 | p 29 of 100
Good: 6301 = 5202 + 1099 | 2091 digits (2379) | Time 746 | running 30 avg 370 | 12:50:43 | p 30 of 100
That was a tough one! The time of 746 was 2.09 times that of the previous running avg 357

Good: 6311 = 4923 + 1388 | 2145 digits (2379) | Time 923 | running 31 avg 388 | 13:06:09 | p 31 of 100
That was a tough one! The time of 923 was 2.49 times that of the previous running avg 370

Good: 6317 = 5960 + 357 | 1965 digits (2379) | Time 290 | running 32 avg 385 | 13:11:02 | p 32 of 100
Good: 6323 = 5789 + 534 | 1998 digits (2379) | Time 367 | running 33 avg 384 | 13:17:09 | p 33 of 100
Good: 6329 = 6239 + 90 | 1922 digits (2379) | Time 132 | running 34 avg 377 | 13:19:21 | p 34 of 100
Good: 6337 = 6317 + 20 | 1912 digits (2379) | Time 85.9 | running 35 avg 369 | 13:20:47 | p 35 of 100
Good: 6343 = 6231 + 112 | 1930 digits (2379) | Time 155 | running 36 avg 363 | 13:23:22 | p 36 of 100
Good: 6353 = 5786 + 567 | 2013 digits (2379) | Time 407 | running 37 avg 364 | 13:30:09 | p 37 of 100
Good: 6359 = 6354 + 5 | 1916 digits (2379) | Time 81.5 | running 38 avg 357 | 13:31:31 | p 38 of 100
Good: 6361 = 5801 + 560 | 2014 digits (2379) | Time 392 | running 39 avg 357 | 13:38:02 | p 39 of 100
Good: 6367 = 6280 + 87 | 1932 digits (2379) | Time 130 | running 40 avg 352 | 13:40:13 | p 40 of 100
Good: 6373 = 6325 + 48 | 1927 digits (2379) | Time 118 | running 41 avg 346 | 13:42:11 | p 41 of 100
Good: 6379 = 6130 + 249 | 1965 digits (2379) | Time 224 | running 42 avg 343 | 13:45:56 | p 42 of 100
Process terminated with an exit code of -2

density = 0.106
8179 = 6301 + 1878 | 2793 digits (1) | 00:39:00.00 | running 1 avg 00:39:00.00 | 03:42:43 | p 1 of 1000
8191 = 7952 + 239 | 2508 digits (2793) | 00:06:44.00 | running 2 avg 00:22:50.00 | 03:49:27 | p 2 of 1000
8209 = 8095 + 114 | 2492 digits (2793) | 00:04:49.00 | running 3 avg 00:16:50.00 | 03:54:15 | p 3 of 1000
8219 = 7008 + 1211 | 2688 digits (2793) | 00:24:30.00 | running 4 avg 00:18:50.00 | 04:18:46 | p 4 of 1000
8221 = 7628 + 593 | 2580 digits (2793) | 00:13:23.00 | running 5 avg 00:17:40.00 | 04:32:09 | p 5 of 1000
8231 = 7152 + 1079 | 2668 digits (2793) | 00:22:00.00 | running 6 avg 00:18:20.00 | 04:54:11 | p 6 of 1000
8233 = 8129 + 104 | 2497 digits (2793) | 00:04:16.00 | running 7 avg 00:16:23.00 | 04:58:26 | p 7 of 1000
8237 = 5391 + 2846 | 2981 digits (2793) | 01:02:40.00 | running 8 avg 00:22:10.00 | 06:01:05 | p 8 of 1000
That was a tough one! The time of 3760 was 3.83 times that of the previous running avg 983

8243 = 7245 + 998 | 2658 digits (2981) | 00:21:20.00 | running 9 avg 00:22:00.00 | 06:22:28 | p 9 of 1000
8263 = 7914 + 349 | 2549 digits (2981) | 00:08:25.00 | running 10 avg 00:20:40.00 | 06:30:54 | p 10 of 1000
8269 = 7995 + 274 | 2538 digits (2981) | 00:07:30.00 | running 11 avg 00:19:30.00 | 06:38:24 | p 11 of 1000
8273 = 7355 + 918 | 2653 digits (2981) | 00:19:00.00 | running 12 avg 00:19:30.00 | 06:57:26 | p 12 of 1000
8287 = 7920 + 367 | 2560 digits (2981) | 00:08:53.00 | running 13 avg 00:18:40.00 | 07:06:19 | p 13 of 1000
8291 = 7850 + 441 | 2574 digits (2981) | 00:09:53.00 | running 14 avg 00:18:00.00 | 07:16:12 | p 14 of 1000
8293 = 7954 + 339 | 2557 digits (2981) | 00:08:50.00 | running 15 avg 00:17:20.00 | 07:25:02 | p 15 of 1000
8297 = 7776 + 521 | 2590 digits (2981) | 00:12:01.00 | running 16 avg 00:17:00.00 | 07:37:04 | p 16 of 1000
8311 = 8135 + 176 | 2533 digits (2981) | 00:05:33.00 | running 17 avg 00:16:24.00 | 07:42:37 | p 17 of 1000
8317 = 8100 + 217 | 2542 digits (2981) | 00:06:15.00 | running 18 avg 00:15:50.00 | 07:48:53 | p 18 of 1000
8329 = 8099 + 230 | 2548 digits (2981) | 00:06:50.00 | running 19 avg 00:15:22.00 | 07:55:43 | p 19 of 1000
8353 = 8085 + 268 | 2562 digits (2981) | 00:07:12.00 | running 20 avg 00:14:57.00 | 08:02:55 | p 20 of 1000
8363 = 7688 + 675 | 2637 digits (2981) | 00:14:47.00 | running 21 avg 00:14:57.00 | 08:17:42 | p 21 of 1000
8369 = 8109 + 260 | 2566 digits (2981) | 00:07:36.00 | running 22 avg 00:14:37.00 | 08:25:18 | p 22 of 1000
8377 = 8016 + 361 | 2586 digits (2981) | 00:09:18.00 | running 23 avg 00:14:23.00 | 08:34:37 | p 23 of 1000
8387 = 8167 + 220 | 2564 digits (2981) | 00:06:45.00 | running 24 avg 00:14:04.00 | 08:41:21 | p 24 of 1000
8389 = 8154 + 235 | 2567 digits (2981) | 00:06:48.00 | running 25 avg 00:13:46.00 | 08:48:10 | p 25 of 1000
8419 = 7869 + 550 | 2632 digits (2981) | 00:12:57.00 | running 26 avg 00:13:44.00 | 09:01:07 | p 26 of 1000
8423 = 7280 + 1143 | 2737 digits (2981) | 00:24:10.00 | running 27 avg 00:14:08.00 | 09:25:13 | p 27 of 1000
8429 = 7821 + 608 | 2645 digits (2981) | 00:14:02.00 | running 28 avg 00:14:07.00 | 09:39:16 | p 28 of 1000
8431 = 7980 + 451 | 2618 digits (2981) | 00:11:38.00 | running 29 avg 00:14:02.00 | 09:50:54 | p 29 of 1000
8443 = 7801 + 642 | 2655 digits (2981) | 00:13:55.00 | running 30 avg 00:14:02.00 | 10:04:49 | p 30 of 1000
8447 = 7337 + 1110 | 2739 digits (2981) | 00:23:20.00 | running 31 avg 00:14:20.00 | 10:28:10 | p 31 of 1000
8461 = 8225 + 236 | 2589 digits (2981) | 00:06:53.00 | running 32 avg 00:14:06.00 | 10:35:03 | p 32 of 1000
8467 = 7467 + 1000 | 2725 digits (2981) | 00:21:20.00 | running 33 avg 00:14:19.00 | 10:56:25 | p 33 of 1000
8501 = 8112 + 389 | 2628 digits (2981) | 00:10:24.00 | running 34 avg 00:14:12.00 | 11:06:48 | p 34 of 1000
8513 = 8454 + 59 | 2574 digits (2981) | 00:04:09.00 | running 35 avg 00:13:55.00 | 11:10:58 | p 35 of 1000
8521 = 8370 + 151 | 2592 digits (2981) | 00:05:41.00 | running 36 avg 00:13:41.00 | 11:16:39 | p 36 of 1000
8527 = 8377 + 150 | 2594 digits (2981) | 00:05:56.00 | running 37 avg 00:13:29.00 | 11:22:35 | p 37 of 1000
8537 = 7939 + 598 | 2676 digits (2981) | 00:14:32.00 | running 38 avg 00:13:30.00 | 11:37:07 | p 38 of 1000
8539 = 8062 + 477 | 2655 digits (2981) | 00:12:19.00 | running 39 avg 00:13:29.00 | 11:49:26 | p 39 of 1000
8543 = 8343 + 200 | 2607 digits (2981) | 00:06:44.00 | running 40 avg 00:13:18.00 | 11:56:11 | p 40 of 1000
8563 = 8541 + 22 | 2582 digits (2981) | 00:03:07.00 | running 41 avg 00:13:04.00 | 11:59:18 | p 41 of 1000
8573 = 7467 + 1106 | 2776 digits (2981) | 00:24:20.00 | running 42 avg 00:13:20.00 | 12:23:34 | p 42 of 1000
8581 = 8542 + 39 | 2591 digits (2981) | 00:03:35.00 | running 43 avg 00:13:06.00 | 12:27:09 | p 43 of 1000
8597 = 6585 + 2012 | 2943 digits (2981) | 00:46:20.00 | running 44 avg 00:13:51.00 | 13:13:33 | p 44 of 1000
That was a tough one! The time of 2780 was 3.54 times that of the previous running avg 786

8599 = 8059 + 540 | 2684 digits (2981) | 00:13:13.00 | running 45 avg 00:13:51.00 | 13:26:46 | p 45 of 1000
8609 = 7364 + 1245 | 2811 digits (2981) | 00:27:30.00 | running 46 avg 00:14:08.00 | 13:54:15 | p 46 of 1000
8623 = 8583 + 40 | 2603 digits (2981) | 00:03:44.00 | running 47 avg 00:13:55.00 | 13:57:59 | p 47 of 1000
8627 = 8235 + 392 | 2667 digits (2981) | 00:10:07.00 | running 48 avg 00:13:50.00 | 14:08:06 | p 48 of 1000
8629 = 8538 + 91 | 2614 digits (2981) | 00:04:47.00 | running 49 avg 00:13:39.00 | 14:12:53 | p 49 of 1000
8641 = 8171 + 470 | 2684 digits (2981) | 00:11:35.00 | running 50 avg 00:13:06.00 | 14:24:28 | p 50 of 1000

Testing 500 primes, from 8761 to 13421 starting at 11:00:38
density = 0.107
8761 = 6390 + 2371 | 3055 digits (1) | 00:58:20.00 | running 1 avg 00:58:20.00 | 11:58:55 | p 1 of 500
8779 = 7903 + 876 | 2797 digits (3055) | 00:21:00.00 | running 2 avg 00:39:40.00 | 12:19:54 | p 2 of 500
8783 = 8090 + 693 | 2766 digits (3055) | 00:17:50.00 | running 3 avg 00:32:20.00 | 12:37:44 | p 3 of 500
8803 = 7130 + 1673 | 2945 digits (3055) | 00:40:50.00 | running 4 avg 00:34:30.00 | 13:18:39 | p 4 of 500
8807 = 8627 + 180 | 2683 digits (3055) | 00:06:42.00 | running 5 avg 00:29:00.00 | 13:25:21 | p 5 of 500
8819 = 6899 + 1920 | 2993 digits (3055) | 00:48:00.00 | running 6 avg 00:32:10.00 | 14:13:25 | p 6 of 500
8821 = 7880 + 941 | 2822 digits (3055) | 00:23:00.00 | running 7 avg 00:30:50.00 | 14:36:26 | p 7 of 500

6863 = 3129 + 3734 | 2724 digits (2296) | 00:59:40.00 |
8761 = 6390 + 2371 | 3055 digits (1) | 00:58:30.00 |

Testing 150 primes, from 8831 to 10169 starting at 01:58:51
density = 0.111
8831 = 8768 + 63 | 2670 digits (1) | 00:04:47.00 | running 1 avg 00:04:47.00 | 02:03:38 | p 1 of 150
8837 = 7394 + 1443 | 2915 digits (2670) | 00:34:40.00 | running 2 avg 00:19:40.00 | 02:38:13 | p 2 of 150
That was a tough one! The time of 2080 was 7.25 times that of the previous running avg 287

8839 = 8605 + 234 | 2703 digits (2915) | 00:07:45.00 | running 3 avg 00:15:44.00 | 02:45:58 | p 3 of 150
8849 = 8655 + 194 | 2698 digits (2915) | 00:07:33.00 | running 4 avg 00:13:41.00 | 02:53:32 | p 4 of 150
8861 = 7626 + 1235 | 2885 digits (2915) | 00:30:10.00 | running 5 avg 00:17:00.00 | 03:23:38 | p 5 of 150
8863 = 5794 + 3069 | 3209 digits (2915) | 01:19:50.00 | running 6 avg 00:27:30.00 | 04:43:30 | p 6 of 150
That was a tough one! The time of 4790 was 4.7 times that of the previous running avg 1020

8867 = 8381 + 486 | 2755 digits (3209) | 00:13:05.00 | running 7 avg 00:25:20.00 | 04:56:36 | p 7 of 150
8887 = 8579 + 308 | 2730 digits (3209) | 00:09:18.00 | running 8 avg 00:23:20.00 | 05:05:53 | p 8 of 150
8893 = 8688 + 205 | 2714 digits (3209) | 00:07:33.00 | running 9 avg 00:21:40.00 | 05:13:27 | p 9 of 150
8923 = 7843 + 1080 | 2877 digits (3209) | 00:26:40.00 | running 10 avg 00:22:10.00 | 05:40:05 | p 10 of 150
8929 = 8400 + 529 | 2782 digits (3209) | 00:14:30.00 | running 11 avg 00:21:30.00 | 05:54:35 | p 11 of 150
8933 = 7308 + 1625 | 2976 digits (3209) | 00:40:50.00 | running 12 avg 00:23:00.00 | 06:35:27 | p 12 of 150
8941 = 7354 + 1587 | 2971 digits (3209) | 00:39:10.00 | running 13 avg 00:24:20.00 | 07:14:33 | p 13 of 150
8951 = 8403 + 548 | 2792 digits (3209) | 00:14:47.00 | running 14 avg 00:23:40.00 | 07:29:19 | p 14 of 150
8963 = 6891 + 2072 | 3063 digits (3209) | 00:52:20.00 | running 15 avg 00:25:30.00 | 08:21:35 | p 15 of 150
8969 = 8524 + 445 | 2779 digits (3209) | 00:13:26.00 | running 16 avg 00:24:50.00 | 08:35:01 | p 16 of 150
8971 = 8947 + 24 | 2705 digits (3209) | 00:03:44.00 | running 17 avg 00:23:30.00 | 08:38:46 | p 17 of 150
8999 = 8619 + 380 | 2776 digits (3209) | 00:11:31.00 | running 18 avg 00:22:50.00 | 08:50:17 | p 18 of 150
9001 = 8956 + 45 | 2718 digits (3209) | 00:04:55.00 | running 19 avg 00:22:00.00 | 08:55:13 | p 19 of 150
9007 = 8520 + 487 | 2798 digits (3209) | 00:13:17.00 | running 20 avg 00:21:30.00 | 09:08:30 | p 20 of 150
9011 = 8826 + 185 | 2746 digits (3209) | 00:07:46.00 | running 21 avg 00:20:50.00 | 09:16:16 | p 21 of 150
9013 = 7271 + 1742 | 3020 digits (3209) | 00:44:50.00 | running 22 avg 00:22:00.00 | 10:01:01 | p 22 of 150
9029 = 8904 + 125 | 2741 digits (3209) | 00:06:21.00 | running 23 avg 00:21:20.00 | 10:07:23 | p 23 of 150
9041 = 8992 + 49 | 2731 digits (3209) | 00:04:45.00 | running 24 avg 00:20:30.00 | 10:12:08 | p 24 of 150
9043 = 9016 + 27 | 2727 digits (3209) | 00:03:55.00 | running 25 avg 00:19:50.00 | 10:16:03 | p 25 of 150
9049 = 8985 + 64 | 2736 digits (3209) | 00:04:45.00 | running 26 avg 00:19:20.00 | 10:20:48 | p 26 of 150
9059 = 6075 + 2984 | 3253 digits (3209) | 01:21:20.00 | running 27 avg 00:21:40.00 | 11:42:06 | p 27 of 150
That was a tough one! The time of 4880 was 4.21 times that of the previous running avg 1160

Testing 150 primes, from 9067 to 10429 starting at 23:30:16
density = 0.109
9067 = 8346 + 721 | 2857 digits (1) | 00:05:26.00 | running 1 avg 00:05:26.00 | 23:35:42 | p 1 of 150
9091 = 8926 + 165 | 2766 digits (2857) | 00:01:18.40 | running 2 avg 00:03:22.00 | 23:37:01 | p 2 of 150
9103 = 8932 + 171 | 2771 digits (2857) | 00:01:29.50 | running 3 avg 00:02:45.00 | 23:38:30 | p 3 of 150
9109 = 8215 + 894 | 2900 digits (2857) | 00:06:15.00 | running 4 avg 00:03:37.00 | 23:44:45 | p 4 of 150
9127 = 8824 + 303 | 2801 digits (2900) | 00:02:22.00 | running 5 avg 00:03:22.00 | 23:47:07 | p 5 of 150
9133 = 8760 + 373 | 2815 digits (2900) | 00:02:41.00 | running 6 avg 00:03:15.00 | 23:49:48 | p 6 of 150
9137 = 8431 + 706 | 2875 digits (2900) | 00:04:53.00 | running 7 avg 00:03:29.00 | 23:54:41 | p 7 of 150
9151 = 8958 + 193 | 2789 digits (2900) | 00:01:29.40 | running 8 avg 00:03:14.00 | 23:56:11 | p 8 of 150
9157 = 7680 + 1477 | 3017 digits (2900) | 00:11:26.00 | running 9 avg 00:04:09.00 | 00:07:37 | p 9 of 150
That was a tough one! The time of 686 was 3.54 times that of the previous running avg 194

9161 = 8766 + 395 | 2828 digits (3017) | 00:02:57.00 | running 10 avg 00:04:02.00 | 00:10:34 | p 10 of 150
9173 = 6638 + 2535 | 3208 digits (3017) | 00:21:30.00 | running 11 avg 00:05:37.00 | 00:32:07 | p 11 of 150
That was a tough one! The time of 1290 was 5.33 times that of the previous running avg 242

9181 = 8160 + 1021 | 2944 digits (3208) | 00:07:36.00 | running 12 avg 00:05:47.00 | 00:39:43 | p 12 of 150
9187 = 8394 + 793 | 2906 digits (3208) | 00:05:38.00 | running 13 avg 00:05:46.00 | 00:45:21 | p 13 of 150
9199 = 9047 + 152 | 2796 digits (3208) | 00:01:12.40 | running 14 avg 00:05:27.00 | 00:46:33 | p 14 of 150
9203 = 8791 + 412 | 2843 digits (3208) | 00:02:48.00 | running 15 avg 00:05:16.00 | 00:49:21 | p 15 of 150
9209 = 9074 + 135 | 2796 digits (3208) | 00:01:09.70 | running 16 avg 00:05:01.00 | 00:50:31 | p 16 of 150
9221 = 9134 + 87 | 2792 digits (3208) | 00:00:47.60 | running 17 avg 00:04:46.00 | 00:51:19 | p 17 of 150
9227 = 9182 + 45 | 2786 digits (3208) | 00:00:36.00 | running 18 avg 00:04:32.00 | 00:51:55 | p 18 of 150
9239 = 8999 + 240 | 2824 digits (3208) | 00:01:49.00 | running 19 avg 00:04:23.00 | 00:53:44 | p 19 of 150
9241 = 8710 + 531 | 2876 digits (3208) | 00:03:48.00 | running 20 avg 00:04:22.00 | 00:57:32 | p 20 of 150
9257 = 9209 + 48 | 2796 digits (3208) | 00:00:36.50 | running 21 avg 00:04:11.00 | 00:58:09 | p 21 of 150
9277 = 9013 + 264 | 2840 digits (3208) | 00:02:06.00 | running 22 avg 00:04:05.00 | 01:00:15 | p 22 of 150
9281 = 9209 + 72 | 2807 digits (3208) | 00:00:53.80 | running 23 avg 00:03:57.00 | 01:01:09 | p 23 of 150
9283 = 8986 + 297 | 2847 digits (3208) | 00:02:23.00 | running 24 avg 00:03:53.00 | 01:03:32 | p 24 of 150
9293 = 8718 + 575 | 2899 digits (3208) | 00:04:18.00 | running 25 avg 00:03:54.00 | 01:07:50 | p 25 of 150
9311 = 9040 + 271 | 2851 digits (3208) | 00:02:07.00 | running 26 avg 00:03:50.00 | 01:09:57 | p 26 of 150
9319 = 7294 + 2025 | 3162 digits (3208) | 00:16:22.00 | running 27 avg 00:04:18.00 | 01:26:19 | p 27 of 150
That was a tough one! The time of 982 was 4.27 times that of the previous running avg 230

9323 = 9042 + 281 | 2856 digits (3208) | 00:02:06.00 | running 28 avg 00:04:13.00 | 01:28:25 | p 28 of 150
9337 = 8301 + 1036 | 2994 digits (3208) | 00:07:59.00 | running 29 avg 00:04:21.00 | 01:36:24 | p 29 of 150
9341 = 9047 + 294 | 2864 digits (3208) | 00:02:26.00 | running 30 avg 00:04:17.00 | 01:38:51 | p 30 of 150
9343 = 8391 + 952 | 2981 digits (3208) | 00:07:28.00 | running 31 avg 00:04:23.00 | 01:46:18 | p 31 of 150
9349 = 9137 + 212 | 2852 digits (3208) | 00:01:45.00 | running 32 avg 00:04:18.00 | 01:48:04 | p 32 of 150
9371 = 8657 + 714 | 2947 digits (3208) | 00:05:25.00 | running 33 avg 00:04:20.00 | 01:53:29 | p 33 of 150
9377 = 8676 + 701 | 2947 digits (3208) | 00:05:36.00 | running 34 avg 00:04:22.00 | 01:59:05 | p 34 of 150
9391 = 8846 + 545 | 2923 digits (3208) | 00:04:20.00 | running 35 avg 00:04:22.00 | 02:03:25 | p 35 of 150
9397 = 8707 + 690 | 2951 digits (3208) | 00:05:34.00 | running 36 avg 00:04:24.00 | 02:08:59 | p 36 of 150
9403 = 8938 + 465 | 2913 digits (3208) | 00:03:27.00 | running 37 avg 00:04:23.00 | 02:12:26 | p 37 of 150
9413 = 7763 + 1650 | 3125 digits (3208) | 00:13:32.00 | running 38 avg 00:04:37.00 | 02:25:58 | p 38 of 150
That was a tough one! The time of 812 was 3.09 times that of the previous running avg 263

9419 = 9337 + 82 | 2850 digits (3208) | 00:00:51.50 | running 39 avg 00:04:31.00 | 02:26:50 | p 39 of 150
9421 = 8866 + 555 | 2934 digits (3208) | 00:04:24.00 | running 40 avg 00:04:31.00 | 02:31:14 | p 40 of 150
9431 = 9358 + 73 | 2852 digits (3208) | 00:00:47.40 | running 41 avg 00:04:26.00 | 02:32:01 | p 41 of 150
9433 = 9431 + 2 | 2840 digits (3208) | 00:00:17.20 | running 42 avg 00:04:20.00 | 02:32:19 | p 42 of 150
9437 = 9432 + 5 | 2842 digits (3208) | 00:00:22.10 | running 43 avg 00:04:14.00 | 02:32:41 | p 43 of 150
9439 = 8513 + 926 | 3005 digits (3208) | 00:07:12.00 | running 44 avg 00:04:18.00 | 02:39:53 | p 44 of 150
9461 = 7985 + 1476 | 3108 digits (3208) | 00:12:25.00 | running 45 avg 00:04:29.00 | 02:52:18 | p 45 of 150
9463 = 8992 + 471 | 2932 digits (3208) | 00:03:40.00 | running 46 avg 00:04:28.00 | 02:55:58 | p 46 of 150
9467 = 8646 + 821 | 2995 digits (3208) | 00:06:37.00 | running 47 avg 00:04:31.00 | 03:02:35 | p 47 of 150
9473 = 8868 + 605 | 2959 digits (3208) | 00:04:52.00 | running 48 avg 00:04:31.00 | 03:07:27 | p 48 of 150
9479 = 9116 + 363 | 2918 digits (3208) | 00:03:01.00 | running 49 avg 00:04:30.00 | 03:10:28 | p 49 of 150
9491 = 8735 + 756 | 2991 digits (3208) | 00:06:00.00 | running 50 avg 00:04:30.00 | 03:16:28 | p 50 of 150
9497 = 8527 + 970 | 3030 digits (3208) | 00:07:50.00 | running 50 avg 00:04:38.00 | 03:24:19 | p 51 of 150
9511 = 9232 + 279 | 2913 digits (3208) | 00:02:19.00 | running 50 avg 00:04:39.00 | 03:26:38 | p 52 of 150
9521 = 9290 + 231 | 2907 digits (3208) | 00:01:56.00 | running 50 avg 00:04:34.00 | 03:28:34 | p 53 of 150
9533 = 9144 + 389 | 2939 digits (3208) | 00:02:55.00 | running 50 avg 00:04:35.00 | 03:31:30 | p 54 of 150
9539 = 8099 + 1440 | 3126 digits (3208) | 00:12:16.00 | running 50 avg 00:04:46.00 | 03:43:46 | p 55 of 150
9547 = 9535 + 12 | 2877 digits (3208) | 00:00:26.60 | running 50 avg 00:04:41.00 | 03:44:13 | p 56 of 150
9551 = 9273 + 278 | 2925 digits (3208) | 00:02:21.00 | running 50 avg 00:04:42.00 | 03:46:34 | p 57 of 150
9587 = 9380 + 207 | 2923 digits (3208) | 00:01:47.00 | running 50 avg 00:04:30.00 | 03:48:21 | p 58 of 150
9601 = 7252 + 2349 | 3304 digits (3208) | 00:22:00.00 | running 50 avg 00:04:53.00 | 04:10:20 | p 59 of 150
That was a tough one! The time of 1320 was 4.89 times that of the previous running avg 270

9613 = 9421 + 192 | 2928 digits (3304) | 00:01:44.00 | running 50 avg 00:04:29.00 | 04:12:05 | p 60 of 150
9619 = 9157 + 462 | 2977 digits (3304) | 00:03:59.00 | running 50 avg 00:04:25.00 | 04:16:03 | p 61 of 150
9623 = 8271 + 1352 | 3135 digits (3304) | 00:11:50.00 | running 50 avg 00:04:32.00 | 04:27:54 | p 62 of 150
9629 = 9077 + 552 | 2996 digits (3304) | 00:04:15.00 | running 50 avg 00:04:36.00 | 04:32:09 | p 63 of 150
9631 = 9016 + 615 | 3008 digits (3304) | 00:05:13.00 | running 50 avg 00:04:39.00 | 04:37:22 | p 64 of 150
9643 = 8168 + 1475 | 3163 digits (3304) | 00:12:57.00 | running 50 avg 00:04:54.00 | 04:50:19 | p 65 of 150
9649 = 7992 + 1657 | 3197 digits (3304) | 00:15:17.00 | running 50 avg 00:05:11.00 | 05:05:35 | p 66 of 150
That was a tough one! The time of 917 was 3.12 times that of the previous running avg 294

9661 = 8692 + 969 | 3079 digits (3304) | 00:08:30.00 | running 50 avg 00:05:21.00 | 05:14:06 | p 67 of 150
9677 = 9234 + 443 | 2992 digits (3304) | 00:03:43.00 | running 50 avg 00:05:23.00 | 05:17:49 | p 68 of 150
9679 = 9555 + 124 | 2936 digits (3304) | 00:01:14.20 | running 50 avg 00:05:20.00 | 05:19:04 | p 69 of 150
9689 = 8813 + 876 | 3071 digits (3304) | 00:07:22.00 | running 50 avg 00:05:28.00 | 05:26:25 | p 70 of 150
9697 = 9062 + 635 | 3031 digits (3304) | 00:05:39.00 | running 50 avg 00:05:33.00 | 05:32:04 | p 71 of 150
9719 = 9603 + 116 | 2947 digits (3304) | 00:01:18.50 | running 50 avg 00:05:33.00 | 05:33:23 | p 72 of 150
9721 = 9519 + 202 | 2962 digits (3304) | 00:02:04.00 | running 50 avg 00:05:33.00 | 05:35:27 | p 73 of 150
9733 = 9715 + 18 | 2934 digits (3304) | 00:00:32.60 | running 50 avg 00:05:28.00 | 05:35:59 | p 74 of 150
9739 = 8744 + 995 | 3107 digits (3304) | 00:08:54.00 | running 50 avg 00:05:37.00 | 05:44:53 | p 75 of 150
9743 = 8520 + 1223 | 3149 digits (3304) | 00:10:26.00 | running 50 avg 00:05:29.00 | 05:55:19 | p 76 of 150
9749 = 9474 + 275 | 2984 digits (3304) | 00:02:24.00 | running 50 avg 00:05:30.00 | 05:57:43 | p 77 of 150
9767 = 9335 + 432 | 3017 digits (3304) | 00:03:40.00 | running 50 avg 00:05:24.00 | 06:01:23 | p 78 of 150
9769 = 8757 + 1012 | 3119 digits (3304) | 00:08:53.00 | running 50 avg 00:05:32.00 | 06:10:16 | p 79 of 150
9781 = 5322 + 4459 | 3730 digits (3304) | 00:50:50.00 | running 50 avg 00:06:25.00 | 07:01:02 | p 80 of 150
A big one!! 3730 digits is 1.13 times the previous largest number of digits 3304

That was a tough one! The time of 3050 was 9.19 times that of the previous running avg 332

9787 = 8665 + 1122 | 3144 digits (3730) | 00:10:03.00 | running 50 avg 00:06:36.00 | 07:11:05 | p 81 of 150
9791 = 9731 + 60 | 2958 digits (3730) | 00:00:53.10 | running 50 avg 00:06:30.00 | 07:11:58 | p 82 of 150
9803 = 9599 + 204 | 2987 digits (3730) | 00:01:55.00 | running 50 avg 00:06:25.00 | 07:13:54 | p 83 of 150
9811 = 8828 + 983 | 3127 digits (3730) | 00:09:00.00 | running 50 avg 00:06:31.00 | 07:22:53 | p 84 of 150
9817 = 8052 + 1765 | 3267 digits (3730) | 00:16:50.00 | running 50 avg 00:06:45.00 | 07:39:39 | p 85 of 150
9829 = 9720 + 109 | 2979 digits (3730) | 00:01:06.40 | running 50 avg 00:06:42.00 | 07:40:46 | p 86 of 150
9833 = 9240 + 593 | 3065 digits (3730) | 00:05:32.00 | running 50 avg 00:06:32.00 | 07:46:18 | p 87 of 150
9839 = 9618 + 221 | 3001 digits (3730) | 00:01:55.00 | running 50 avg 00:06:34.00 | 07:48:13 | p 88 of 150
9851 = 9277 + 574 | 3067 digits (3730) | 00:05:17.00 | running 50 avg 00:06:35.00 | 07:53:30 | p 89 of 150
9857 = 9512 + 345 | 3029 digits (3730) | 00:03:14.00 | running 50 avg 00:06:38.00 | 07:56:45 | p 90 of 150
9859 = 9529 + 330 | 3026 digits (3730) | 00:03:06.00 | running 50 avg 00:06:41.00 | 07:59:51 | p 91 of 150
9871 = 9050 + 821 | 3117 digits (3730) | 00:07:24.00 | running 50 avg 00:06:50.00 | 08:07:15 | p 92 of 150
9883 = 9658 + 225 | 3015 digits (3730) | 00:02:09.00 | running 50 avg 00:06:44.00 | 08:09:24 | p 93 of 150
9887 = 9447 + 440 | 3054 digits (3730) | 00:03:56.00 | running 50 avg 00:06:33.00 | 08:13:20 | p 94 of 150
9901 = 8982 + 919 | 3143 digits (3730) | 00:08:11.00 | running 50 avg 00:06:39.00 | 08:21:32 | p 95 of 150
9907 = 3717 + 6190 | 4073 digits (3730) | 01:23:20.00 | running 50 avg 00:08:13.00 | 09:44:47 | p 96 of 150
That was a tough one! The time of 5000 was 12.5 times that of the previous running avg 399

9923 = 9848 + 75 | 3001 digits (4073) | 00:01:03.60 | running 50 avg 00:08:08.00 | 09:45:51 | p 97 of 150
9929 = 9825 + 104 | 3008 digits (4073) | 00:01:07.20 | running 50 avg 00:08:06.00 | 09:46:58 | p 98 of 150
9931 = 9370 + 561 | 3089 digits (4073) | 00:04:53.00 | running 50 avg 00:08:04.00 | 09:51:51 | p 99 of 150
9941 = 9500 + 441 | 3071 digits (4073) | 00:04:06.00 | running 50 avg 00:08:00.00 | 09:55:58 | p 100 of 150
9949 = 9725 + 224 | 3035 digits (4073) | 00:02:08.00 | running 50 avg 00:08:00.00 | 09:58:05 | p 101 of 150
9967 = 9654 + 313 | 3056 digits (4073) | 00:03:03.00 | running 50 avg 00:08:01.00 | 10:01:09 | p 102 of 150
9973 = 9706 + 267 | 3050 digits (4073) | 00:02:34.00 | running 50 avg 00:08:00.00 | 10:03:43 | p 103 of 150
10007 = 9860 + 147 | 3039 digits (4073) | 00:01:40.00 | running 50 avg 00:07:47.00 | 10:05:23 | p 104 of 150
10009 = 7865 + 2144 | 3391 digits (4073) | 00:21:20.00 | running 50 avg 00:08:13.00 | 10:26:48 | p 105 of 150
10037 = 9174 + 863 | 3174 digits (4073) | 00:08:20.00 | running 50 avg 00:08:20.00 | 10:35:07 | p 106 of 150
10039 = 9654 + 385 | 3090 digits (4073) | 00:03:31.00 | running 50 avg 00:08:23.00 | 10:38:39 | p 107 of 150
10061 = 9897 + 164 | 3058 digits (4073) | 00:01:34.50 | running 50 avg 00:07:57.00 | 10:40:14 | p 108 of 150
10067 = 9821 + 246 | 3074 digits (4073) | 00:02:20.00 | running 50 avg 00:07:58.00 | 10:42:33 | p 109 of 150
10069 = 10056 + 13 | 3034 digits (4073) | 00:00:27.10 | running 50 avg 00:07:54.00 | 10:43:01 | p 110 of 150
10079 = 8704 + 1375 | 3277 digits (4073) | 00:13:31.00 | running 50 avg 00:07:56.00 | 10:56:32 | p 111 of 150
10091 = 7430 + 2661 | 3507 digits (4073) | 00:29:00.00 | running 50 avg 00:08:26.00 | 11:25:36 | p 112 of 150
That was a tough one! The time of 1740 was 3.66 times that of the previous running avg 476

10093 = 10011 + 82 | 3053 digits (4073) | 00:01:05.00 | running 50 avg 00:08:21.00 | 11:26:41 | p 113 of 150
10099 = 8712 + 1387 | 3285 digits (4073) | 00:13:44.00 | running 50 avg 00:08:22.00 | 11:40:25 | p 114 of 150
10103 = 8473 + 1630 | 3329 digits (4073) | 00:16:15.00 | running 50 avg 00:08:23.00 | 11:56:40 | p 115 of 150
10111 = 7913 + 2198 | 3431 digits (4073) | 00:23:10.00 | running 50 avg 00:08:41.00 | 12:19:55 | p 116 of 150
10133 = 10128 + 5 | 3052 digits (4073) | 00:00:21.90 | running 50 avg 00:08:37.00 | 12:20:17 | p 117 of 150
10139 = 8142 + 1997 | 3404 digits (4073) | 00:20:50.00 | running 50 avg 00:09:01.00 | 12:41:04 | p 118 of 150
10141 = 10041 + 100 | 3071 digits (4073) | 00:01:11.30 | running 50 avg 00:08:54.00 | 12:42:15 | p 119 of 150
10151 = 9840 + 311 | 3111 digits (4073) | 00:03:11.00 | running 50 avg 00:08:51.00 | 12:45:26 | p 120 of 150
10159 = 9612 + 547 | 3155 digits (4073) | 00:05:29.00 | running 50 avg 00:08:56.00 | 12:50:55 | p 121 of 150
10163 = 10004 + 159 | 3088 digits (4073) | 00:01:56.00 | running 50 avg 00:08:56.00 | 12:52:51 | p 122 of 150
10169 = 9590 + 579 | 3164 digits (4073) | 00:05:34.00 | running 50 avg 00:09:02.00 | 12:58:25 | p 123 of 150
10177 = 9448 + 729 | 3192 digits (4073) | 00:07:05.00 | running 50 avg 00:08:59.00 | 13:05:30 | p 124 of 150
10181 = 10004 + 177 | 3096 digits (4073) | 00:01:59.00 | running 50 avg 00:08:49.00 | 13:07:30 | p 125 of 150
10193 = 9145 + 1048 | 3253 digits (4073) | 00:10:09.00 | running 50 avg 00:08:59.00 | 13:17:39 | p 126 of 150
10211 = 9697 + 514 | 3165 digits (4073) | 00:04:43.00 | running 50 avg 00:09:00.00 | 13:22:22 | p 127 of 150
10223 = 9106 + 1117 | 3275 digits (4073) | 00:11:40.00 | running 50 avg 00:09:03.00 | 13:34:02 | p 128 of 150
10243 = 9683 + 560 | 3183 digits (4073) | 00:05:35.00 | running 50 avg 00:08:08.00 | 13:39:37 | p 129 of 150
10247 = 10115 + 132 | 3108 digits (4073) | 00:01:29.50 | running 50 avg 00:07:57.00 | 13:41:07 | p 130 of 150
10253 = 9936 + 317 | 3143 digits (4073) | 00:03:17.00 | running 50 avg 00:08:00.00 | 13:44:23 | p 131 of 150
10259 = 8778 + 1481 | 3350 digits (4073) | 00:15:04.00 | running 50 avg 00:08:16.00 | 13:59:27 | p 132 of 150
10267 = 9898 + 369 | 3156 digits (4073) | 00:03:42.00 | running 50 avg 00:08:10.00 | 14:03:10 | p 133 of 150
10271 = 6488 + 3783 | 3759 digits (4073) | 00:46:20.00 | running 50 avg 00:08:46.00 | 14:49:30 | p 134 of 150
That was a tough one! The time of 2780 was 5.67 times that of the previous running avg 490

10273 = 10113 + 160 | 3121 digits (4073) | 00:01:49.00 | running 50 avg 00:08:47.00 | 14:51:20 | p 135 of 150
10289 = 9012 + 1277 | 3323 digits (4073) | 00:13:10.00 | running 50 avg 00:08:56.00 | 15:04:30 | p 136 of 150
10301 = 10175 + 126 | 3124 digits (4073) | 00:01:27.20 | running 50 avg 00:08:56.00 | 15:05:57 | p 137 of 150
10303 = 9603 + 700 | 3225 digits (4073) | 00:07:16.00 | running 50 avg 00:08:58.00 | 15:13:13 | p 138 of 150
10313 = 10191 + 122 | 3127 digits (4073) | 00:01:33.00 | running 50 avg 00:08:56.00 | 15:14:46 | p 139 of 150
10321 = 9606 + 715 | 3233 digits (4073) | 00:07:19.00 | running 50 avg 00:09:01.00 | 15:22:06 | p 140 of 150
10331 = 10121 + 210 | 3147 digits (4073) | 00:02:17.00 | running 50 avg 00:08:55.00 | 15:24:23 | p 141 of 150
10333 = 10175 + 158 | 3139 digits (4073) | 00:01:53.00 | running 50 avg 00:08:55.00 | 15:26:16 | p 142 of 150
10337 = 10250 + 87 | 3128 digits (4073) | 00:01:11.50 | running 50 avg 00:08:51.00 | 15:27:28 | p 143 of 150
10343 = 9738 + 605 | 3221 digits (4073) | 00:06:20.00 | running 50 avg 00:08:49.00 | 15:33:48 | p 144 of 150
10357 = 9847 + 510 | 3208 digits (4073) | 00:05:17.00 | running 50 avg 00:07:14.00 | 15:39:06 | p 145 of 150
10369 = 8689 + 1680 | 3418 digits (4073) | 00:18:20.00 | running 50 avg 00:07:35.00 | 15:57:21 | p 146 of 150
10391 = 9276 + 1115 | 3325 digits (4073) | 00:11:03.00 | running 50 avg 00:07:47.00 | 16:08:24 | p 147 of 150
10399 = 9940 + 459 | 3212 digits (4073) | 00:04:41.00 | running 50 avg 00:07:47.00 | 16:13:05 | p 148 of 150
10427 = 8796 + 1631 | 3427 digits (4073) | 00:17:30.00 | running 50 avg 00:08:03.00 | 16:30:39 | p 149 of 150
10429 = 9082 + 1347 | 3377 digits (4073) | 00:14:05.00 | running 50 avg 00:08:18.00 | 16:44:45 | p 150 of 150

==========================================================

BEFORE
8831 = 8768 + 63 | 2670 digits (1) | 00:04:47.00 | running 1 avg 00:04:47.00 | 02:03:38 | p 1 of 150
8837 = 7394 + 1443 | 2915 digits (2670) | 00:34:40.00 | running 2 avg 00:19:40.00 | 02:38:13 | p 2 of 150
8839 = 8605 + 234 | 2703 digits (2915) | 00:07:45.00 | running 3 avg 00:15:44.00 | 02:45:58 | p 3 of 150
8849 = 8655 + 194 | 2698 digits (2915) | 00:07:33.00 | running 4 avg 00:13:41.00 | 02:53:32 | p 4 of 150
8861 = 7626 + 1235 | 2885 digits (2915) | 00:30:10.00 | running 5 avg 00:17:00.00 | 03:23:38 | p 5 of 150
8863 = 5794 + 3069 | 3209 digits (2915) | 01:19:50.00 | running 6 avg 00:27:30.00 | 04:43:30 | p 6 of 150
8867 = 8381 + 486 | 2755 digits (3209) | 00:13:05.00 | running 7 avg 00:25:20.00 | 04:56:36 | p 7 of 150
8887 = 8579 + 308 | 2730 digits (3209) | 00:09:18.00 | running 8 avg 00:23:20.00 | 05:05:53 | p 8 of 150
8893 = 8688 + 205 | 2714 digits (3209) | 00:07:33.00 | running 9 avg 00:21:40.00 | 05:13:27 | p 9 of 150
8923 = 7843 + 1080 | 2877 digits (3209) | 00:26:40.00 | running 10 avg 00:22:10.00 | 05:40:05 | p 10 of 150

AFTER changing gmpy.is_prime's probability argument from 100 to 25 AND moving the import of gmpy within my
isPrime() function to the top of mycalc.py.

These primes will be tested: [8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923]
Testing 10 primes, from 8831 to 8923 starting at 18:30:03
density = 0.108
8831 = 8768 + 63 | 2670 digits (1) | 00:00:39.10 | running 1 avg 00:00:39.10 | 18:30:43 | p 1 of 10
8837 = 7394 + 1443 | 2915 digits (2670) | 00:09:55.00 | running 2 avg 00:05:17.00 | 18:40:38 | p 2 of 10
8839 = 8605 + 234 | 2703 digits (2915) | 00:01:36.70 | running 3 avg 00:04:04.00 | 18:42:15 | p 3 of 10
8849 = 8655 + 194 | 2698 digits (2915) | 00:01:32.60 | running 4 avg 00:03:26.00 | 18:43:48 | p 4 of 10
8861 = 7626 + 1235 | 2885 digits (2915) | 00:08:42.00 | running 5 avg 00:04:29.00 | 18:52:30 | p 5 of 10
8863 = 5794 + 3069 | 3209 digits (2915) | 00:24:40.00 | running 6 avg 00:07:51.00 | 19:17:12 | p 6 of 10
8867 = 8381 + 486 | 2755 digits (3209) | 00:03:17.00 | running 7 avg 00:07:12.00 | 19:20:29 | p 7 of 10
8887 = 8579 + 308 | 2730 digits (3209) | 00:02:06.00 | running 8 avg 00:06:34.00 | 19:22:35 | p 8 of 10
8893 = 8688 + 205 | 2714 digits (3209) | 00:01:30.00 | running 9 avg 00:06:00.00 | 19:24:05 | p 9 of 10
8923 = 7843 + 1080 | 2877 digits (3209) | 00:07:26.00 | running 10 avg 00:06:08.00 | 19:31:31 | p 10 of 10
================================================


tested primes to 10429: odd int Failures: 3615
"""