through the n = 28 barrier!

=====================================================================================
The script started at 07:16:48
The time now is       08:18:01
n = 27
last_n = 40
mp.dps = 50

1.6449340668482260712236801656065464306267967617728 prev_upper_bound_partial_sum
                 |
1.6449340668482263451602314163861554995709116163483 upper_bound_partial_sum
         |
1.6449340593976458117930113570853939658758527249461 euler_series_partial_sum
         |
1.6449340484646558565791839881848273411389395815047 lower_bound_partial_sum
         |
1.6449340300810850940615853092038901137628526920855 prev_lower_bound_partial_sum



1.6449340668482264364724151666460251892189499012068 pi_squared_over_6
         |
1.6449340593976458117930113570853939658758527249461 euler_series_partial_sum
          |
1.6449340519470651316024559026766294448373576673147 prev_euler_series_partial_sum



upper_bound_partial_sum - euler_series_partial_sum  (should approach 0 as limit):
0.0000000074505805333672200593007615336950588914021522129695

euler_series_partial_sum - lower_bound_partial_sum  (should approach 0 as limit):
0.000000010932989955213827368900566624736913143441494693901
(If either of the above differences are negative, then there is a bug in this demo, or the proof is false.)

pi_squared_over_6 - upper_bound_partial_sum  (should approach 0 as limit):
9.1312183750259869689648038284858500887346758157783e-17

pi_squared_over_6 - lower_bound_partial_sum  (should approach 0 as limit):
0.000000018383570579893231178461197848080010319702147794217



3.1415926535897932384626433832795028841971693993751 pi
         |
3.1415926464750128184716330923063917724990199167573 sqrt_of__6_times_euler_series_partial_sum

for n = 27  time was 1.003 hours  or  01:00:10.63
Total time was 2.023 hours  or  02:01:23.64
=====================================================================================
The script started at 07:16:48
The time now is       09:18:12
n = 28
last_n = 40
mp.dps = 50

1.6449340668482263451602314163861554995709116163483 prev_upper_bound_partial_sum
1.6449340668482263451602314163861554995709116163483 upper_bound_partial_sum
          |
1.6449340631229361310716071916223320974772137196339 euler_series_partial_sum
         |
1.6449340576564409639014320768956868858828681716387 lower_bound_partial_sum
         |
1.6449340484646558565791839881848273411389395815047 prev_lower_bound_partial_sum



1.6449340668482264364724151666460251892189499012068 pi_squared_over_6
          |
1.6449340631229361310716071916223320974772137196339 euler_series_partial_sum
         |
1.6449340593976458117930113570853939658758527249461 prev_euler_series_partial_sum



upper_bound_partial_sum - euler_series_partial_sum  (should approach 0 as limit):
0.0000000037252902140886242247638234020936978967143998710502

euler_series_partial_sum - lower_bound_partial_sum  (should approach 0 as limit):
0.000000005466495167170175114726645211594345547995170904258
(If either of the above differences are negative, then there is a bug in this demo, or the proof is false.)

pi_squared_over_6 - upper_bound_partial_sum  (should approach 0 as limit):
9.1312183750259869689648038284858500887346758157783e-17

pi_squared_over_6 - lower_bound_partial_sum  (should approach 0 as limit):
0.000000009191785472570983089750338303336081729568071662655



3.1415926535897932384626433832795028841971693993751 pi
          |
3.141592650032403037107403659242742499789555914797 sqrt_of__6_times_euler_series_partial_sum

for n = 28  time was 2.878 hours  or  02:52:40.29
Total time was 4.901 hours  or  04:54:03.94
=====================================================================================
The script started at 07:16:48
The time now is       12:10:52
n = 29
last_n = 40
mp.dps = 50

1.6449340668482263451602314163861554995709116163483 prev_upper_bound_partial_sum
1.6449340668482263451602314163861554995709116163483 upper_bound_partial_sum
          |
1.6449340649855812855067346583421600055452706355577 euler_series_partial_sum
          |
1.6449340622523336545308317466409211927268898939935 lower_bound_partial_sum
         |
1.6449340576564409639014320768956868858828681716387 prev_lower_bound_partial_sum



1.6449340668482264364724151666460251892189499012068 pi_squared_over_6
          |
1.6449340649855812855067346583421600055452706355577 euler_series_partial_sum
          |
1.6449340631229361310716071916223320974772137196339 prev_euler_series_partial_sum



upper_bound_partial_sum - euler_series_partial_sum  (should approach 0 as limit):
0.0000000018626450596534967580439954940256409807906372229934

euler_series_partial_sum - lower_bound_partial_sum  (should approach 0 as limit):
0.0000000027332476309759029117012388128183807415641495010431
(If either of the above differences are negative, then there is a bug in this demo, or the proof is false.)

pi_squared_over_6 - upper_bound_partial_sum  (should approach 0 as limit):
9.1312183750259869689648038284858500887346758157783e-17

pi_squared_over_6 - lower_bound_partial_sum  (should approach 0 as limit):
0.0000000045958927819415834200051039964920600072132876113832



3.1415926535897932384626433832795028841971693993751 pi
          |
3.1415926518110981399450898698690926244628019007573 sqrt_of__6_times_euler_series_partial_sum

for n = 29  time was 6.123 hours  or  06:07:24.20
Total time was 11.024 hours  or  11:01:28.16
=====================================================================================
The script started at 07:16:48
The time now is       18:18:17
n = 30
last_n = 40
mp.dps = 50