I corrected my powering modulo a prime routine. I added Pollard’s p – 1 factoring method and Shanks-Mestre elliptic curve point counting algorithm.
number to be tested or 0 to quit:
10000019
number of primes in factor base:
10000
Prime sieving time = 3.220000
N[0] = 10000019
a = 7838973
b = 2449531
m = 9995356
q = 356977
P = (9786147, 3226544)
P1 = (0, 1)
P2 = (5887862, 8051455)
N[1] = 356977
a = 45561
b = 178451
m = 357946
q = 178973
P = (80627, 163299)
P1 = (0, 1)
P2 = (52101, 282559)
N[2] = 178973
a = 135281
b = 76426
m = 178996
q = 73
P = (10238, 98035)
P1 = (0, 1)
P2 = (46702, 94326)
number is proven prime
runtime in seconds = 35.471000
number to be tested or 0 to quit:
10015969
number of primes in factor base:
10000
Prime sieving time = 3.424000
N[0] = 10015969
a = 6613193
b = 3951715
m = 10013908
q = 2503477
P = (998314, 8329764)
P1 = (0, 1)
P2 = (6944357, 1053776)
N[1] = 2503477
a = 1175442
b = 379813
m = 2505736
q = 293
P = (646462, 1631861)
P1 = (0, 1)
P2 = (1477980, 88719)
number is proven prime
runtime in seconds = 5.612000
number to be tested or 0 to quit:
99997981
number of primes in factor base:
10000
Prime sieving time = 4.152000
N[0] = 99997981
a = 34129462
b = 80482974
m = 100001414
q = 181
P = (19305995, 40493835)
P1 = (0, 1)
P2 = (33828245, 72969559)
number is proven prime
runtime in seconds = 11.500000
number to be tested or 0 to quit:
100001819
number of primes in factor base:
100000
Prime sieving time = 3.218000
N[0] = 100001819
a = 2694060
b = 17329746
m = 100008102
q = 5569
P = (124594, 14596756)
P1 = (0, 1)
P2 = (32514144, 56926555)
number is proven prime
runtime in seconds = 76.301000
number to be tested or 0 to quit:
100005317
number of primes in factor base:
100000
Prime sieving time = 3.269000
N[0] = 100005317
a = 45478318
b = 328034
m = 99988256
q = 3124633
P = (62548529, 30179124)
P1 = (0, 1)
P2 = (70379514, 76899689)
N[1] = 3124633
a = 2605576
b = 1809212
m = 3127654
q = 503
P = (1236288, 2081401)
P1 = (0, 1)
P2 = (2264479, 2583693)
number is proven prime
runtime in seconds = 459.979000
number to be tested or 0 to quit:
100000007
number of primes in factor base:
100000
Prime sieving time = 3.209000
N[0] = 100000007
a = 50593669
b = 72502607
m = 100005736
q = 2053
P = (72365335, 69885097)
P1 = (0, 1)
P2 = (55023241, 20078454)
number is proven prime
runtime in seconds = 163.705000
number to be tested or 0 to quit:
100014437
number of primes in factor base:
100000
Prime sieving time = 3.919000
N[0] = 100014437
a = 49955472
b = 45482796
m = 100024160
q = 263
P = (41650735, 8652103)
P1 = (0, 1)
P2 = (53790105, 37282431)
number is proven prime
runtime in seconds = 12.915000
Author: jamespatewilliamsjr
My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.
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Numerical Explorations 