M2277857 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	2⁶⁸	26.1671	67.6471%	2800000	82000000	0.6783	7.5243%	26.8454	70.0814%	2.4343%
PrimeNet	2⁵⁸	0.0169	62.0690%	10000	190000	0.0019	2.9228%	0.0187	63.1776%	1.1086%
GPU72	2⁶²	0.2697	64.5161%	12000	190000	0.0021	1.7089%	0.2718	65.1225%	0.6064%
Difference	+6	+25.8974	+3.1309%	+2788000	+81810000	+0.6763	+5.8154%	+26.5736	+4.9589%	+4.9589%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2277857	5198068676148035762303	22	72.138	1140999780966943 27409 × 41628654127	2020-07-21	27409	41628654127	816.40	216.23	403.86

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.229%
2010-11-06T16:28:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.200%
2010-11-14T13:24:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.358%
2011-01-01T00:28:00	markr	tiny	105000	2152500		-		-	-	0.021	-	-	2.453%
2014-09-15T22:12:00	ANONYMOUS	Manual testing	133177	133177		-		-	-	0.013	-	-	0.954%
2016-03-20T01:38:12	Jocelyn Larouche	Manual testing	272160	272160		-		-	-	0.026	-	-	1.386%
2016-04-07T01:57:19	Jocelyn Larouche	Manual testing	326592	5878656	12	-		-	-	0.060	-	-	3.703%
2016-04-15T08:53:50	Jocelyn Larouche	Manual testing	326592	11831037	6	-		-	-	0.091	-	-	4.266%
2018-08-30T21:10:23	Jocelyn Larouche	low 4M	653184	653184		-		-	-	0.062	-	-	2.053%
2018-09-03T21:22:19	Jocelyn Larouche	low 4M	653184	1306368		-		-	-	0.066	-	-	2.659%
2018-09-05T22:37:59	Jocelyn Larouche	low 4M	653184	1959552		-		-	-	0.069	-	-	3.017%
2018-09-12T22:59:12	Jocelyn Larouche	low 4M	653184	3265920		-		-	-	0.076	-	-	3.475%
2019-03-05T20:04:56	King	No.1_FactorFinder	2800000	82000000	6	-		-	-	0.678	-	-	7.524%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:11	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.067	-	-
2009-01-10T21:17:00	Sturle Sunde	gouffy.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-06T18:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.135	-	-
2013-12-06T02:47:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.431	-	-
2015-03-10T10:45:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.862	-	-
2015-03-10T10:45:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.640	-	-
2015-11-01T21:51:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.281	-	-
2017-02-13T09:31:36	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	6.561	-	-
2019-04-22T13:11:37	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.12	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.139 GHz-days
Estimated T-Level:	4.150

Digits	B1	Curves	Complete	FacMiss
20	11000	83 / 100	0.830	43.423%
25	50000	83 / 280	0.296	74.307%

New Calculation Method

Total ECM effort:	7.139 GHz-days
Estimated T-Level:	4.150

Digits	B1	Complete	FacMiss
20	11000	2.677	6.874%
25	50000	0.242	78.507%
30	250000	0.015	98.521%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		81	6.967
50000	5000000	5198068676148035762303	2	0.172

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-05T11:07:00	oodaira	Win02	50000	5000000						3	0.258
2010-06-21T10:48:00	James Hintz	nana	50000	5000000						3	0.258
2011-11-08T04:26:00	S36049	Wolle5	50000	5000000						3	0.258
2013-08-28T15:31:00	arnaud	srv-630	50000	5000000						3	0.258
2015-04-07T15:32:00	Bruce	desk16	50000	5000000						3	0.258
2016-02-11T18:09:39	Hartmut Birr	C7CE7B89E	50000	5000000						3	0.258
2016-04-08T15:44:12	Bruce	Desk6	50000	5000000						3	0.258
2016-07-27T16:27:37	Bruce	Desk6	50000	5000000						3	0.258
2016-12-17T05:58:17	Bruce	Desk6	50000	5000000						3	0.258
2017-07-25T00:31:18	Bruce	Desk6	50000	5000000						3	0.258
2017-12-30T13:43:43	Bruce	Desk6	50000	5000000						3	0.258
2018-06-21T02:54:45	Bruce	Desk6	50000	5000000						3	0.258
2019-08-06T20:35:15	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.258
2020-02-29T11:00:34	mnd9	kitchen	50000	5000000						3	0.258
2020-03-06T13:05:59	mat10243x	K3	50000	5000000						3	0.258
2020-03-14T00:35:00	mnd9	office2	50000	5000000						3	0.258
2020-03-22T01:36:24	Alvin Bunk	BADCAT	50000	5000000						3	0.258
2020-04-03T17:31:11	Brett Walker	brain	50000	5000000						3	0.258
2020-04-17T09:39:23	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.258
2020-04-26T04:22:25	Keysarecool	Boat_Anchor	50000	5000000						3	0.258
2020-05-04T15:25:50	Keysarecool	Boat_Anchor	50000	5000000						3	0.258
2020-05-16T03:09:08	mnd9	eileen	50000	5000000						3	0.258
2020-06-02T21:32:25	Summy	CHB	50000	5000000						3	0.258
2020-06-22T05:07:02	Nesowa	6700T	50000	5000000						3	0.258
2020-07-01T23:24:35	GAN	AC-KL	50000	5000000						3	0.258
2020-07-08T08:50:48	GAN	LMS-11	50000	5000000						3	0.258
2020-07-14T10:34:01	GAN	LMS-13	50000	5000000						3	0.258
2020-07-20T13:39:18	GAN	LMS-08	50000	5000000	5198068676148035762303	72.138	2	2	4261944215765176	2	0.172

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	773EAFAB5BC553F6	0.150

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 2800000, B2 = 82000000 (P-1 stage 2)

B1 = 2800000 (P-1 stage 1)

B1 = 326592, B2 = 11831037 (P-1 stage 2)

B1 = 653184, B2 = 3265920 (P-1 stage 2)

B1 = 653184, B2 = 1959552 (P-1 stage 2)

B1 = 653184, B2 = 1306368 (P-1 stage 2)

B1 = 653184 (P-1 stage 1)

B1 = 326592, B2 = 5878656 (P-1 stage 2)

B1 = 326592 (P-1 stage 1)

B1 = 272160 (P-1 stage 1)

B1 = 105000, B2 = 2152500 (P-1 stage 2)

B1 = 133177 (P-1 stage 1)

B1 = 105000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

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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