Homework

Problem 1.Some Primes:

The 24th Prime is :89;
The 101st Prime is :547;
The 251st Prime is:1597;


Problem 2.Some Fibonacci Primes:

The 24th Prime :89 is in Fibonacci's numbers at 11th possition;
The 101st Prime:547 is not in Fibonacci's numbers;
The 251st Prime :1597 is in Fibonacci's numbers at 17th possition;


Problem 3.Some Factorials:

100! is :933262154439441526816992388
562667004907159682643816214685929638
952175999932299156089414639761565182
862536979208272237582511852109168640
00000000000000000000000

171! is :124101807021766782342484052
410310399261660557750169318538895180
361199607522169175299275197812048758
557646495950167038705280988985869071
076733124203221848436431047357788996
854827829075454156196485215346831804
429323959817369689965723590394761615
227855818006117636510842880000000000
0000000000000000000000000000000

250! is :323285626090910773232081455
202436847099484371767378066674794242
711282374755511120948881791537102819
945092850735318943292673093171280899
082279103027907128192167652724018926
473321804118626100683292536513367893
908956993571353017504051317876007724
793306540233900616482555224881943657
258605739922264125483298220484913772
177665064127685880715312897877767295
191399084437747870258917297325515028
324178732065818848206247858265980884
882554880000000000000000000000000000
0000000000000000000000000000000000

Problem 4.Calculate Hypotenuse:

1.Catheri: a = 3 and b = 4:
c = \sqrt ( a^2 + b^2 );
c = \sqrt (9 + 16);
c = \sqrt 25;
c = 5;


2.Catheti: a = 10 and b = 12
 c = \sqrt ( a^2 + b^2 );
c = \sqrt (100 + 144);
c = \sqrt 244;
c = 15.620499351813;


3.Catheti: a = 100 and b = 250
 c = \sqrt ( a^2 + b^2 );
c = \sqrt (10000 + 62500);
c = \sqrt 72500;
c = 269.25824035673;


Problem 5.Numeral System Conversions:

1234d to binary:   1234:2=617|0
                    617:2=308|1
                    308:2=154|0
                    154:2=77 |0
                     77:2=38 |1
                     38:2=19 |0   ____ 10011010010
                     19:2=9  |1
                      9:2=4  |1
                      4:2=2  |0
                      2:2=1  |0
                      1:2=0  |1


1234d to hexadecimal: 1234:16=77|2
                        77:16=4 |D ------ 4D2
                         4:16=0 |4


1100101b to decimal: 1×2⁶+1×2⁵+0×2⁴+0×2³+1×2²+0×2¹+1×2⁰ = 101
1100101b to Hex:  64


ABChex to decimal:10×16²+11×16¹+12×16⁰ = 2748
ABChex to binary :101010111100

Problem 6.Least Common Multiple:
LCM(1234,3456) :2132352