p-1 issue with Prime95

error · 2019-07-19, 20:16

There seems to be a problem with p-1 test on certain numbers by Prime95.
I'm testing numbers of the form 2*3^n+1 (Williams numbers MP 3).
p-1 test by Prime95 fails to find most of the smooth factors for such numbers.

Examples: {exponent n, factor p, {factors of p-1}}

Code:

{3475646, 119489318533691, {2, 5, 7, 431, 8011, 494387}}
{7665700, 119491953091009, {3, 29, 31, 64, 163, 1451, 2927}}
{9257944, 119531331540809, {8, 11, 1289, 30313, 34763}}
{6423342, 119605774137529, {3, 8, 49, 53, 14087, 136223}}
{3042101, 119808015836737, {3, 64, 277, 34231, 65809}}
{5838880, 119973320941321, {5, 7, 8, 11, 27, 33857, 42611}}
{5012801, 120053607739783, {2, 3, 101, 463, 4057, 105467}}
{4070145, 120089496622181, {4, 5, 361, 487, 1399, 24413}}
{9086412, 120111987466147, {2, 3, 13, 67, 71, 1681, 192571}}
{7266064, 120126224537833, {3, 8, 2729, 7649, 239783}}
{8105957, 120156817371103, {2, 27, 29, 41, 10303, 181639}}
{6926322, 120167197804937, {8, 17, 61, 139, 2063, 50513}}
{3012802, 120188143840001, {61, 256, 313, 625, 39343}}
{7129212, 120222226105171, {2, 3, 5, 7, 3041, 10243, 18379}}
{9166614, 120243245621777, {16, 29, 31, 41, 83, 241, 10193}}
{7625410, 120375431852843, {2, 14783, 25541, 159407}}
{3361126, 120383218522649, {8, 41, 167, 4421, 497113}}
{6792312, 120394103284001, {13, 32, 49, 125, 149, 337, 941}}
{4546184, 120400176592907, {2, 7, 89, 263, 2441, 150517}}
{9997324, 120412055355299, {2, 49, 673, 26987, 67651}}
{8382020, 120475635536401, {3, 16, 25, 53, 97, 2843, 6869}}
{6717329, 120559382021839, {2, 3, 541, 1019, 3019, 12073}}
{5020722, 120585793479313, {3, 7, 16, 97, 36629, 101009}}
{8632670, 120659693453987, {2, 863, 1109, 1543, 40853}}
{9136786, 120682062140921, {5, 7, 8, 23, 37, 1663, 304553}}
{6799072, 120766589012273, {7, 16, 53, 383, 3181, 16699}}
{8566642, 120787899533723, {2, 23, 1187, 8191, 270071}}
{4605525, 120894933211081, {3, 5, 8, 23, 49, 97, 971, 9491}}

Only the last of these is found by Prime95 with bounds B1=40000, B2=500000.

worktodo.txt

Code:

Pminus1=2,3,3475646,1,40000,500000
Pminus1=2,3,7665700,1,40000,500000
Pminus1=2,3,9257944,1,40000,500000
Pminus1=2,3,6423342,1,40000,500000
Pminus1=2,3,3042101,1,40000,500000
Pminus1=2,3,5838880,1,40000,500000
Pminus1=2,3,5012801,1,40000,500000
Pminus1=2,3,4070145,1,40000,500000
Pminus1=2,3,9086412,1,40000,500000
Pminus1=2,3,7266064,1,40000,500000
Pminus1=2,3,8105957,1,40000,500000
Pminus1=2,3,6926322,1,40000,500000
Pminus1=2,3,3012802,1,40000,500000
Pminus1=2,3,7129212,1,40000,500000
Pminus1=2,3,9166614,1,40000,500000
Pminus1=2,3,7625410,1,40000,500000
Pminus1=2,3,3361126,1,40000,500000
Pminus1=2,3,6792312,1,40000,500000
Pminus1=2,3,4546184,1,40000,500000
Pminus1=2,3,9997324,1,40000,500000
Pminus1=2,3,8382020,1,40000,500000
Pminus1=2,3,6717329,1,40000,500000
Pminus1=2,3,5020722,1,40000,500000
Pminus1=2,3,8632670,1,40000,500000
Pminus1=2,3,9136786,1,40000,500000
Pminus1=2,3,6799072,1,40000,500000
Pminus1=2,3,8566642,1,40000,500000
Pminus1=2,3,4605525,1,40000,500000

results.txt

Code:

[Fri Jul 19 18:23:27 2019]
UID: error/flow, 2*3^3475646+1 completed P-1, B1=40000, B2=500000, Wh4: 5A1CBB19
UID: error/flow, 2*3^9166614+1 completed P-1, B1=40000, B2=500000, Wh4: ED3B5FF0
[Fri Jul 19 18:29:59 2019]
UID: error/flow, 2*3^7665700+1 completed P-1, B1=40000, B2=500000, Wh4: C64715E3
UID: error/flow, 2*3^7625410+1 completed P-1, B1=40000, B2=500000, Wh4: C5601B94
[Fri Jul 19 18:36:50 2019]
UID: error/flow, 2*3^3361126+1 completed P-1, B1=40000, B2=500000, Wh4: 570ABF63
UID: error/flow, 2*3^9257944+1 completed P-1, B1=40000, B2=500000, Wh4: EF905B7E
[Fri Jul 19 18:42:06 2019]
UID: error/flow, 2*3^6423342+1 completed P-1, B1=40000, B2=500000, Wh4: A65AC518
UID: error/flow, 2*3^6792312+1 completed P-1, B1=40000, B2=500000, Wh4: AFCC3BDF
UID: error/flow, 2*3^3042101+1 completed P-1, B1=40000, B2=500000, Wh4: 4EC448C9
UID: error/flow, 2*3^4546184+1 completed P-1, B1=40000, B2=500000, Wh4: 75A292BD
[Fri Jul 19 18:48:09 2019]
UID: error/flow, 2*3^5838880+1 completed P-1, B1=40000, B2=500000, Wh4: 972BDCBB
UID: error/flow, 2*3^5012801+1 completed P-1, B1=40000, B2=500000, Wh4: 81B5FC8A
UID: error/flow, 2*3^9997324+1 completed P-1, B1=40000, B2=500000, Wh4: 02A9BFD6
[Fri Jul 19 18:55:21 2019]
UID: error/flow, 2*3^4070145+1 completed P-1, B1=40000, B2=500000, Wh4: 6979A00F
UID: error/flow, 2*3^8382020+1 completed P-1, B1=40000, B2=500000, Wh4: D8F7794E
[Fri Jul 19 19:02:24 2019]
UID: error/flow, 2*3^9086412+1 completed P-1, B1=40000, B2=500000, Wh4: EB32621A
UID: error/flow, 2*3^6717329+1 completed P-1, B1=40000, B2=500000, Wh4: ADF83EAC
[Fri Jul 19 19:07:43 2019]
UID: error/flow, 2*3^7266064+1 completed P-1, B1=40000, B2=500000, Wh4: BBF5246E
UID: error/flow, 2*3^5020722+1 completed P-1, B1=40000, B2=500000, Wh4: 8202FF58
[Fri Jul 19 19:14:20 2019]
UID: error/flow, 2*3^8105957+1 completed P-1, B1=40000, B2=500000, Wh4: D1B204E1
UID: error/flow, 2*3^8632670+1 completed P-1, B1=40000, B2=500000, Wh4: DF727081
[Fri Jul 19 19:19:45 2019]
UID: error/flow, 2*3^6926322+1 completed P-1, B1=40000, B2=500000, Wh4: B340368D
UID: error/flow, 2*3^9136786+1 completed P-1, B1=40000, B2=500000, Wh4: EC765C3F
UID: error/flow, 2*3^3012802+1 completed P-1, B1=40000, B2=500000, Wh4: 4DF049F0
[Fri Jul 19 19:26:47 2019]
UID: error/flow, 2*3^6799072+1 completed P-1, B1=40000, B2=500000, Wh4: AFE03B9C
UID: error/flow, 2*3^7129212+1 completed P-1, B1=40000, B2=500000, Wh4: B8772EA1
[Fri Jul 19 19:31:58 2019]
UID: error/flow, 2*3^8566642+1 completed P-1, B1=40000, B2=500000, Wh4: DDC37634
P-1 found a factor in stage #2, B1=40000, B2=500000.
UID: error/flow, 2*3^4605525+1 has a factor: 120894933211081 (P-1, B1=40000, B2=500000)

Does this problem influence other kind of numbers?
Is the PRP test for these numbers free of errors?

Prime95 · 2019-07-20, 01:36

I will look into this when I get a chance, but it will likely be at least a week.

ixfd64 · 2019-07-20, 01:53

George, are you on vacation?

We're starting to itch for another new Mersenne prime.

kriesel · 2019-07-20, 09:15

Quote:

Originally Posted by ixfd64

George, are you on vacation?

We're starting to itch for another new Mersenne prime.

Patience; lately it's been on his year-end holiday vacation.

Prime95 · 2019-07-27, 02:37

Will be fixed in 29.8 build 6

error · 2019-07-27, 06:54

Quote:

Originally Posted by Prime95

Will be fixed in 29.8 build 6

What was the problem?
PRP tests with earlier versions still good?

Prime95 · 2019-07-27, 16:59

The problem was in the P-1 code. The bug has been there forever.

Your previous PRP tests are all good.

pepi37 · 2019-07-27, 17:06

Quote:

Originally Posted by Prime95

The problem was in the P-1 code. The bug has been there forever.

Your previous PRP tests are all good.

When can we expect build 6?

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2019-07-20, 01:36	#2
Prime95 P90 years forever! Aug 2002 Yeehaw, FL 17·487 Posts	I will look into this when I get a chance, but it will likely be at least a week.

2019-07-20, 01:53	#3
ixfd64 Bemusing Prompter "Danny" Dec 2002 California 2³·313 Posts	George, are you on vacation? We're starting to itch for another new Mersenne prime.

2019-07-27, 02:37	#5
Prime95 P90 years forever! Aug 2002 Yeehaw, FL 17×487 Posts	Will be fixed in 29.8 build 6

2019-07-27, 16:59	#7
Prime95 P90 years forever! Aug 2002 Yeehaw, FL 17·487 Posts	The problem was in the P-1 code. The bug has been there forever. Your previous PRP tests are all good.