M2418781 Mersenne number exponent details

is 2 ^2418781 - 1

has 728126 decimal digits

takes 0.163 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷⁰	98.7897	68.5714%	3102822	43439508	0.5192	5.7743%	99.3089	70.3862%	1.8148%
PrimeNet	2⁵⁹	0.0317	62.7119%	10000	180000	0.0019	2.5222%	0.0336	63.6523%	0.9405%
GPU72	2⁶³	0.6598	65.0794%	10000	140000	0.0017	1.2769%	0.6615	65.5253%	0.4459%
Difference	+7	+98.1298	+3.4921%	+3092822	+43299508	+0.5175	+4.4974%	+98.6474	+4.8609%	+4.8609%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2418781	4436196297029546676959263	25	81.876	917031409009237851 3 × 7 × 15889 × 2748326662079	2020-07-14	15889	2748326662079	304,627	14,668	27,395

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.150%
2010-11-09T22:13:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.140%
2010-11-16T23:09:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.183%
2010-12-18T23:28:00	markr	tiny	95000	1923750		-		-	-	0.019	-	-	1.851%
2014-04-04T12:25:00	mikr	MSI	3102822	43439508		-		-	-	0.519	-	-	5.774%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.016	-	-
1998-04-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.016	-	-
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2016-02-23T16:29:14	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.032	-	-
2009-01-11T17:07:00	Sturle Sunde	othello.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-
2012-06-04T15:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.127	-	-
2013-01-23T08:28:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.406	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.812	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.545	-	-
2015-10-22T10:17:20	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.089	-	-
2017-07-05T06:34:28	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.179	-	-
2019-04-03T13:27:27	Anton Repko	Manual testing	2⁶⁷	2⁶⁹		-	-	37.07	-	-
2019-04-20T09:26:45	Anton Repko	Manual testing	2⁶⁹	2⁷⁰		-	-	49.43	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.614 GHz-days
Estimated T-Level:	3.150

Digits	B1	Curves	Complete	FacMiss
20	11000	63 / 100	0.630	53.091%
25	50000	63 / 280	0.225	79.819%

New Calculation Method

Total ECM effort:	5.614 GHz-days
Estimated T-Level:	3.150

Digits	B1	Complete	FacMiss
20	11000	2.032	13.104%
25	50000	0.184	83.221%
30	250000	0.011	98.875%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		60	5.347
50000	5000000	4436196297029546676959263	3	0.267

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-05T14:32:00	Martti Järvi	Mardeni	50000	5000000						3	0.267
2010-02-25T13:23:00	unconnected	X3220--xp	50000	5000000						3	0.267
2012-03-09T20:13:00	S36049	Wolle5	50000	5000000						3	0.267
2013-12-08T08:18:00	Andy Incline	Office-PC	50000	5000000						3	0.267
2015-07-01T00:37:00	guru	w6	50000	5000000						3	0.267
2016-02-20T01:42:24	Sintax	cloud2	50000	5000000						3	0.267
2016-06-05T05:23:15	Bruce	Desk6	50000	5000000						3	0.267
2016-10-01T13:45:24	Bruce	Desk6	50000	5000000						3	0.267
2017-04-12T01:17:49	Bruce	Desk6	50000	5000000						3	0.267
2017-11-14T14:47:19	Sebastian Hornbostel	V2	50000	5000000						3	0.267
2018-04-17T18:45:56	Bruce	Desk6	50000	5000000						3	0.267
2018-10-22T22:53:15	Bruce	Desk6	50000	5000000						3	0.267
2019-07-26T04:47:02	Hans Loeblich	Manual testing	50000	5000000						3	0.267
2020-04-26T05:14:12	nordi	sweet16	50000	5000000						3	0.267
2020-05-04T23:31:07	mnd9	colab	50000	5000000						3	0.267
2020-05-15T19:44:29	Summy	CHB	50000	5000000						3	0.267
2020-06-03T04:07:23	Sergey Nosov	TS140-02	50000	5000000						3	0.267
2020-06-22T00:58:11	IanGlencross	glenx24	50000	5000000						3	0.267
2020-07-02T21:48:54	GAN	KL-SCH07	50000	5000000						3	0.267
2020-07-08T05:48:00	lycorn	colab_ES	50000	5000000						3	0.267
2020-07-14T08:44:02	GAN	LMS-13	50000	5000000	4436196297029546676959263	81.876	3	2	899719111073524	3	0.267

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-02-08T00:00:00	ANONYMOUS	v4_computers	A363B3279070918E	0.163
1998-04-11T00:00:00	ANONYMOUS	v4_computers	A363B3279070918E	0.163
1999-04-13T00:00:00	ANONYMOUS	v4_computers	A363B3279070918E	0.163
2018-05-19T14:43:24	kkmrkkblmbrbk	old	A363B3279070918E	0.163

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-14T12:42:40

CrypticClue

Manual testing

4436196297029546676959263

DF2BD6250CE7493A

2020-07-14T14:21:23

oodaira

com2

4436196297029546676959263

DF2BD6250CE7493A

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 = 3102822, B2 = 43439508 (P-1 stage 2)

B1 = 3102822 (P-1 stage 1)

B1 = 95000, B2 = 1923750 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-07-14T14:21:23+00:00

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