M1251697 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	23.7389	68.6567%	300000	10000000	0.0381	4.1839%	23.7770	69.9681%	1.3114%
PrimeNet	2⁵⁶	0.0077	62.5000%	5500	90000	0.0005	2.4371%	0.0081	63.4139%	0.9139%
GPU72	2⁶⁰	0.1227	65.0000%	5000	32000	0.0003	0.8556%	0.1230	65.2995%	0.2995%
Difference	+7	+23.6162	+3.6567%	+295000	+9968000	+0.0378	+3.3283%	+23.6540	+4.6686%	+4.6686%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1251697	11434017275069887509073	23	73.276	4567406199371688 2³ × 3 × 11787439 × 16145033	2013-09-12	11787439	16145033	1,623.5	0.5526	1.1025
1251697	5752417761462920888954839	25	82.250	2297847546755692827 3 × 7² × 15631615964324441	2018-02-02	49	15631615964324441	1,234,233	39,139,395	73,101,491

exponent	prime factors	composite factor	digits	bits*
1251697	11434017275069887509073 5752417761462920888954839	65773244057985888864763912054223637536099754247	47	155.526

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.238%
2003-11-28T00:00:00	eteo	v4_computers	200000	2000000		-		-	-	0.014	-	-	2.761%
2016-03-17T19:03:44	alpertron	Manual testing	300000	10000000	12	-		-	-	0.038	-	-	4.184%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.015	-	-
2003-06-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.031	-	-
2022-03-07T17:32:03	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.092	-	-
2009-02-17T01:10:00	Sturle Sunde	gilia.ifi	2⁶⁰	2⁶¹		-	-	0.123	-	-
2011-05-09T14:41:00	Xyzzy	Manual testing	2⁶¹	2⁶²		-	-	0.245	-	-
2012-10-07T08:33:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.784	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.177 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	324 / 100	3.240	3.853%
25	50000	324 / 280	1.157	31.373%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	19.177 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.769	0.000%
25	50000	1.616	19.866%
30	250000	0.131	87.697%
35	1000000	0.009	99.130%

ECM Summary

B1	B2	factor	curves	GHz-days
		11434017275069887509073	1	0.00000e+0
50000	5000000		236	9.052
50000	5000000	5752417761462920888954839	44	1.688
250000	25000000		44	8.438

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-11-09T06:26:00	Chad Davis	Bayes	50000	5000000						1	0.038
2008-08-25T18:48:00	Sturle Sunde	v21	50000	5000000						3	0.115
2009-02-01T20:09:00	Sturle Sunde	v21	50000	5000000						3	0.115
2009-07-03T15:44:00	Geoff Wing	GW1	50000	5000000						3	0.115
2009-10-13T02:01:00	Lupo	yorick	50000	5000000						3	0.115
2010-03-21T04:03:00	ClknGo Software Corp	cngs1	50000	5000000						3	0.115
2010-12-21T13:07:00	Lackó	Iroda_Eva	50000	5000000						3	0.115
2011-10-01T14:29:00	James Hintz	chris3	50000	5000000						3	0.115
2012-06-27T18:06:00	OS1	Tina	50000	5000000						3	0.115
2012-11-27T05:39:00	Salvetay	server5	50000	5000000						3	0.115
2013-09-12T20:26:00	jim f in mn	asus			11434017275069887509073	73.276		1		1	-
2018-02-02T17:08:59	TJAOI	Manual testing	50000	5000000	5752417761462920888954839	82.250	44	2		44	1.688
2018-02-02T17:08:59	TJAOI	Manual testing	50000	5000000						67	2.570
2018-10-05T13:08:39	TJAOI	Manual testing	50000	5000000						141	5.408
2021-03-05T18:05:59	TJAOI	Manual testing	250000	25000000						44	8.438

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-29T18:54:20

Oliver Kruse

GTX-2

11434017275069887509073

D421C86FE92F87__

2017-10-20T17:49:50

kkmrkkblmbrbk

c4.xlarge

11434017275069887509073

D421C86FE92F87__

2018-02-02T20:07:01

MaximeG

MSI_GS63VR

11434017275069887509073

5752417761462920888954839

DAEB5224259695__

2018-02-09T02:26:19

Oliver Kruse

GTX-3

11434017275069887509073

5752417761462920888954839

DAEB5224259695__

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 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 200000, B2 = 2000000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

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