(75*10^3-57)/99
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(75*10^3-57)/99
N=757
*** N is prime!
Time: 0 sec
(75*10^17-57)/99
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(75*10^17-57)/99
N=75757575757575757
Factor: 2^2 divides N - 1
Factor: 2 divides N + 1
Factor: 3 divides N - 1
Factor: 11 divides N - 1
Factor: 53 divides N - 1
Factor: 149 divides N + 1
Factorization results: F1=0.2278 F2=0.1466
F1=6996
F2=298
Pass: gcd(5^((N-1)/2) - 1, N) = 1: R20=75757575757575755
Pass: 5^(N-1) = 1 (mod N): R20=1
Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=1 q=-1 R20=0
Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=3 q=1 R20=0
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=5 q=5 R20=2
Pass: U{N+1} = 0 (mod N): d=5 p=5 q=5 R20=0
Fail: gcd(5^((N-1)/3) - 1, N) not = 1: R20=0
Fail: gcd(7^((N-1)/3) - 1, N) not = 1: R20=0
Pass: gcd(13^((N-1)/3) - 1, N) = 1: R20=63242172398142789
Pass: 13^(N-1) = 1 (mod N): R20=1
Pass: gcd(13^((N-1)/11) - 1, N) = 1: R20=43901163972662109
Pass: gcd(13^((N-1)/53) - 1, N) = 1: R20=7556654713222190
Pass: gcd(U{(N+1)/149}, N) = 1: d=5 p=5 q=5 R20=61703462868850100
BLS tests passed: F1=0.2278 F2=0.1466
Main divisor test: F1=0.2278 F2=0.1287 G=0.3565 S=0.0000 T=1
G=1042404
Main divisor test passed: 1/1
Final divisor test: F=0.2278 G=0.3565 H=0.8121 t=-1 a=743
Final divisor test passed: 1487/1487 r=1476 i=0
*** N is prime!
Time: 0 sec
(75*10^1079-57)/99
== BPI:B2641029AD510 ============================================
TITANIX 2.1.0 - Primality Certificate
Started 07.23.2001 at 12:08:21 PM
Running time 2h 18mn 19s
Candidate certified prime
=================================================================
Proved prime with Titanix by Hans Rosenthal.
The zipped file "757_539.zip" is 114 KB.
When unpacked the file "Titanix-B2641029AD510-001.out" is 273 KB.
The zip file is available on demand by simple email request.
(75*10^1415-57)/99
== BPI:B2632003161A4 ============================================
TITANIX 2.1.0 - Primality Certificate
Started 07.08.2001 at 12:53:56 AM
Running time 7h 13mn 6s
Candidate certified prime
=================================================================
Proved prime with Titanix by Hans Rosenthal.
The zipped file "757_707.zip" is 180 KB.
When unpacked the file "Titanix-B2632003161A4-001.out" is 426 KB.
The zip file is available on demand by simple email request.
(75*10^13265-57)/99
By Hans Rosenthal
PFGW 1.1 test for probable primality in bases
3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61 and 251
(75*10^13265-57)/99 is 3-PRP! (49.480000 seconds)
(75*10^13265-57)/99 is 5-PRP! (49.540000 seconds)
(75*10^13265-57)/99 is 7-PRP! (49.440000 seconds)
(75*10^13265-57)/99 is 11-PRP! (49.430000 seconds)
(75*10^13265-57)/99 is 13-PRP! (49.490000 seconds)
(75*10^13265-57)/99 is 17-PRP! (49.490000 seconds)
(75*10^13265-57)/99 is 19-PRP! (49.550000 seconds)
(75*10^13265-57)/99 is 23-PRP! (50.530000 seconds)
(75*10^13265-57)/99 is 29-PRP! (49.540000 seconds)
(75*10^13265-57)/99 is 31-PRP! (49.590000 seconds)
(75*10^13265-57)/99 is 37-PRP! (49.480000 seconds)
(75*10^13265-57)/99 is 41-PRP! (50.310000 seconds)
(75*10^13265-57)/99 is 43-PRP! (49.480000 seconds)
(75*10^13265-57)/99 is 47-PRP! (49.430000 seconds)
(75*10^13265-57)/99 is 53-PRP! (49.540000 seconds)
(75*10^13265-57)/99 is 59-PRP! (49.490000 seconds)
(75*10^13265-57)/99 is 61-PRP! (49.490000 seconds)
(75*10^13265-57)/99 is 251-PRP! (49.490000 seconds)
(75*10^14579-57)/99
By Hans Rosenthal
PFGW 1.1 test for probable primality in bases
3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61 and 251
(75*10^14579-57)/99 is 3-PRP! (54.380000 seconds)
(75*10^14579-57)/99 is 5-PRP! (54.380000 seconds)
(75*10^14579-57)/99 is 7-PRP! (54.430000 seconds)
(75*10^14579-57)/99 is 11-PRP! (54.430000 seconds)
(75*10^14579-57)/99 is 13-PRP! (54.380000 seconds)
(75*10^14579-57)/99 is 17-PRP! (54.380000 seconds)
(75*10^14579-57)/99 is 19-PRP! (54.320000 seconds)
(75*10^14579-57)/99 is 23-PRP! (55.470000 seconds)
(75*10^14579-57)/99 is 29-PRP! (54.600000 seconds)
(75*10^14579-57)/99 is 31-PRP! (54.380000 seconds)
(75*10^14579-57)/99 is 37-PRP! (54.320000 seconds)
(75*10^14579-57)/99 is 41-PRP! (54.320000 seconds)
(75*10^14579-57)/99 is 43-PRP! (54.380000 seconds)
(75*10^14579-57)/99 is 47-PRP! (54.330000 seconds)
(75*10^14579-57)/99 is 53-PRP! (54.320000 seconds)
(75*10^14579-57)/99 is 59-PRP! (54.330000 seconds)
(75*10^14579-57)/99 is 61-PRP! (54.370000 seconds)
(75*10^14579-57)/99 is 251-PRP! (54.380000 seconds)
(75*10^15293-57)/99
By Hans Rosenthal
PFGW 1.1 test for probable primality in bases
3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61 and 251
(75*10^15293-57)/99 is 3-PRP! (57.070000 seconds)
(75*10^15293-57)/99 is 5-PRP! (57.120000 seconds)
(75*10^15293-57)/99 is 7-PRP! (57.060000 seconds)
(75*10^15293-57)/99 is 11-PRP! (57.070000 seconds)
(75*10^15293-57)/99 is 13-PRP! (57.230000 seconds)
(75*10^15293-57)/99 is 17-PRP! (57.120000 seconds)
(75*10^15293-57)/99 is 19-PRP! (57.120000 seconds)
(75*10^15293-57)/99 is 23-PRP! (57.120000 seconds)
(75*10^15293-57)/99 is 29-PRP! (57.180000 seconds)
(75*10^15293-57)/99 is 31-PRP! (57.120000 seconds)
(75*10^15293-57)/99 is 37-PRP! (57.070000 seconds)
(75*10^15293-57)/99 is 41-PRP! (57.130000 seconds)
(75*10^15293-57)/99 is 43-PRP! (57.070000 seconds)
(75*10^15293-57)/99 is 47-PRP! (57.070000 seconds)
(75*10^15293-57)/99 is 53-PRP! (57.060000 seconds)
(75*10^15293-57)/99 is 59-PRP! (57.070000 seconds)
(75*10^15293-57)/99 is 61-PRP! (57.060000 seconds)
(75*10^15293-57)/99 is 251-PRP! (57.120000 seconds)
(75*10^41657-57)/99
By Ray Chandler
PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14]
Primality testing (75*10^41657-57)/99 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 4+sqrt(5)
(75*10^41657-57)/99 is Fermat and Lucas PRP! (500.2901s+0.0028s)
(75*10^72941-57)/99
By Ray Chandler
PFGW Version 3.4.6.64BIT.20110307.Win_Dev [GWNUM 26.5]
Primality testing (75*10^72941-57)/99 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
(75*10^72941-57)/99 is Fermat and Lucas PRP! (1897.1641s+0.0259s)
[
TOP OF PAGE]
( © All rights reserved ) - Last modified : March 18, 2023.
Patrick De Geest - Belgium
- Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com