M172871 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	171.8849	73.1343%	100000000	2000000000	1.3607	12.2015%	173.2457	76.4123%	3.2780%
PrimeNet	2⁴⁰	0.0000	55.0000%	1900	40000	0.0000	11.5847%	0.0000	60.2131%	5.2131%
GPU72	2⁴⁴	0.0000	59.0909%	3200	65000	0.0000	8.0949%	0.0001	62.4024%	3.3115%
Difference	+23	+171.8849	+14.0434%	+99996800	+1999935000	+1.3607	+4.1066%	+173.2456	+14.0099%	+14.0099%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
172871	3317137771737077334009863	25	81.456	9594257486036053861 157 × 181 × 1163 × 1559 × 186211849	2009-01-21	1559	186211849	3,937,297	0.0678	0.1267

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2001-05-06T00:00:00	ANONYMOUS	v4_computers	100000	10000000		-		-	-	0.004	-	-	2.564%
2002-06-02T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.001	-	-	1.452%
2002-07-27T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.003	-	-	2.103%
2003-02-09T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.006	-	-	2.883%
2003-10-08T00:00:00	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.011	-	-	3.779%
2017-05-07T09:01:59	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-	skipped known factor: 3317137771737077334009863	-	-	1.361	-	-	12.201%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1999-11-10T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.003	-	-
2000-04-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.014	-	-
2022-03-07T04:17:12	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.014	-	-
2001-01-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.056	-	-
2002-06-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.111	-	-
2022-03-07T04:17:12	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.111	-	-
2008-12-30T10:58:00	Sturle Sunde	hummel.ifi	2⁵⁸	2⁵⁹		-	-	0.222	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.193 GHz-days
Estimated T-Level:	29.445

Digits	B1	Curves	Complete	FacMiss
20	11000	848 / 100	8.480	0.020%
25	50000	848 / 280	3.029	4.812%
30	250000	569 / 640	0.889	41.076%

New Calculation Method

Total ECM effort:	15.193 GHz-days
Estimated T-Level:	29.445

Digits	B1	Complete	FacMiss
20	11000	62.458	0.000%
25	50000	9.007	0.012%
30	250000	0.948	38.769%
35	1000000	0.078	92.507%
40	3000000	0.005	99.480%

ECM Summary

B1	B2	factor	curves	GHz-days
		3317137771737077334009863	1	0.00000e+0
50000	5000000		279	1.357
250000	25000000		569	13.84

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-01T22:03:00	George Woltman	D_P4Debug	50000	5000000						1	0.005
2007-08-11T23:49:00	drew	messier	50000	5000000						1	0.005
2007-08-17T08:05:00	ANONYMOUS	Bayes	50000	5000000						1	0.005
2007-08-25T03:44:00	Team_Bundu	bundu1	50000	5000000						1	0.005
2007-09-01T03:23:00	Chad Davis	Bayes	50000	5000000						1	0.005
2007-09-09T15:17:00	Chad Davis	Bayes	50000	5000000						1	0.005
2007-09-26T04:54:00	James Heinrich	WHS	50000	5000000						1	0.005
2007-11-11T06:44:00	ANONYMOUS	minister	50000	5000000						1	0.005
2007-11-15T02:32:00	George Woltman	x32-debug	50000	5000000						1	0.005
2008-01-12T16:35:00	Steve Scott	Celeron	50000	5000000						3	0.015
2008-01-21T12:47:00	Steve Scott	Abit-3	50000	5000000						3	0.015
2008-02-03T07:19:00	Steve Scott	Abit-1	50000	5000000						3	0.015
2008-04-08T19:32:00	Sturle Sunde	v17	50000	5000000						3	0.015
2008-08-24T05:18:00	Sturle Sunde	v22	50000	5000000						3	0.015
2008-09-13T14:29:00	Sturle Sunde	v21	50000	5000000						3	0.015
2008-09-24T20:15:00	Sturle Sunde	v1	50000	5000000						3	0.015
2008-10-16T17:23:00	Sturle Sunde	v23	50000	5000000						3	0.015
2008-11-06T11:13:00	Jayson King	atlas	50000	5000000						3	0.015
2008-11-24T17:59:00	Sturle Sunde	v21	50000	5000000						3	0.015
2008-12-07T12:33:00	Sturle Sunde	v17	50000	5000000						3	0.015
2008-12-31T04:06:00	Sturle Sunde	v22	50000	5000000						3	0.015
2009-01-21T02:24:00	axn	Manual testing			3317137771737077334009863	81.456		1		1	-
2014-06-12T17:52:00	TJAOI	Manual testing	50000	5000000						3	0.015
2014-12-12T13:35:00	TJAOI	Manual testing	50000	5000000						50	0.243
2015-06-26T10:33:00	TJAOI	Manual testing	50000	5000000						90	0.438
2016-07-22T12:39:28	TJAOI	Manual testing	50000	5000000						91	0.443
2017-05-12T15:29:08	TJAOI	Manual testing	250000	25000000						44	1.070
2018-05-30T02:14:57	Yxinity	MacBook	250000	25000000						3	0.073
2018-05-30T17:15:04	Yxinity	Manual testing	250000	25000000						3	0.073
2018-05-31T17:43:21	Yxinity	Manual testing	250000	25000000						3	0.073
2018-06-03T09:46:48	Yxinity	Manual testing	250000	25000000						3	0.073
2018-06-04T18:35:41	Yxinity	Manual testing	250000	25000000						3	0.073
2018-06-09T18:43:23	Yxinity	Manual testing	250000	25000000						3	0.073
2018-08-19T14:46:33	Yxinity	Manual testing	250000	25000000						3	0.073
2018-09-05T15:54:39	Yxinity	Manual testing	250000	25000000						3	0.073
2018-09-20T13:21:30	Niels_Mache_Nextcloud	SuperDry-X	250000	25000000						3	0.073
2018-09-20T18:47:08	Niels_Mache_Nextcloud	SuperDry3	250000	25000000						3	0.073
2018-09-21T03:01:01	Niels_Mache_Nextcloud	SuperDry-JP	250000	25000000						3	0.073
2018-09-21T14:54:43	Niels_Mache_Nextcloud	SuperDry-JP	250000	25000000						3	0.073