M2172539 Mersenne number exponent details

is 2 ^2172539 - 1

has 654000 decimal digits

takes 0.143 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	2⁶⁸	27.4356	67.6471%	5000000	200000000	1.4896	8.9466%	28.9252	70.5415%	2.8945%
PrimeNet	2⁵⁸	0.0177	62.0690%	10000	180000	0.0018	2.8565%	0.0195	63.1525%	1.0835%
GPU72	2⁶²	0.2828	64.5161%	11000	160000	0.0018	1.5677%	0.2846	65.0724%	0.5563%
Difference	+6	+27.1528	+3.1309%	+4989000	+199840000	+1.4877	+7.3789%	+28.6405	+5.4691%	+5.4691%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2172539	141623817478505572926989807	27	86.872	32594079433903274677 13 × 7061983 × 355032981463	2020-04-21	7061983	355032981463	9,144,826	1,844.8	3,444.3

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.226%
2010-11-05T01:16:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.198%
2010-11-07T17:05:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.354%
2011-01-15T16:06:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.514%
2011-01-15T20:31:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.203%
2014-06-11T02:11:00	Jocelyn Larouche	Manual testing	119543	119543		-		-	-	0.011	-	-	0.889%
2014-10-05T22:22:00	Jocelyn Larouche	Manual testing	149086	149086		-		-	-	0.014	-	-	1.007%
2015-12-19T12:11:00	HBendtz	Manual testing	700000	21000000	12	-		-	-	0.172	-	-	5.204%
2019-11-07T16:53:04	mikr	MSI	5000000	200000000	12	-		-	-	1.490	-	-	8.947%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:07	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-05T01:27:00	Sturle Sunde	bakeng.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-07T11:50:00	Sturle Sunde	celair.ifi	2⁶¹	2⁶²		-	-	0.141	-	-
2013-09-09T08:39:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.452	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.904	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.720	-	-
2016-01-02T13:50:56	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.440	-	-
2016-11-14T03:44:01	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.879	-	-
2019-04-29T13:20:34	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.76	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.154 GHz-days
Estimated T-Level:	3.600

Digits	B1	Curves	Complete	FacMiss
20	11000	72 / 100	0.720	48.499%
25	50000	72 / 280	0.257	77.290%

New Calculation Method

Total ECM effort:	6.154 GHz-days
Estimated T-Level:	3.600

Digits	B1	Complete	FacMiss
20	11000	2.323	9.802%
25	50000	0.210	81.066%
30	250000	0.013	98.716%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		69	5.897
50000	5000000	141623817478505572926989807	3	0.256

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-21T04:55:00	Never Odd Or Even	T_Quad	50000	5000000						3	0.256
2009-12-03T22:55:00	James Hintz	ryan	50000	5000000						3	0.256
2011-08-26T02:19:00	Bud	annan	50000	5000000						3	0.256
2013-05-10T10:42:00	ANONYMOUS		50000	5000000						3	0.256
2015-02-17T08:58:00	arnaud	CHAMOT22	50000	5000000						3	0.256
2015-10-14T12:37:32	lopper	i5-4670	50000	5000000						3	0.256
2016-03-04T13:04:05	Bruce	Desk6	50000	5000000						3	0.256
2016-06-22T22:21:32	Bruce	test	50000	5000000						3	0.256
2016-10-18T00:03:05	Bruce	Desk6	50000	5000000						3	0.256
2017-04-02T10:00:35	Bruce	Desk6	50000	5000000						3	0.256
2017-10-29T09:47:08	Bruce	Desk6	50000	5000000						3	0.256
2018-03-06T11:12:19	Bruce	Desk6	50000	5000000						3	0.256
2018-08-17T20:37:45	Bruce	Desk6	50000	5000000						3	0.256
2020-01-24T18:53:11	Yuji HASEGAWA	sx1w7	50000	5000000						3	0.256
2020-02-01T15:20:56	J.R. Allen	lapacer	50000	5000000						3	0.256
2020-02-10T09:42:12	tom9358	dttom	50000	5000000						3	0.256
2020-02-17T08:06:21	EricP	Cannonfodder	50000	5000000						3	0.256
2020-02-24T16:22:50	daveward2005	Davy	50000	5000000						3	0.256
2020-03-03T00:02:26	kracker	O0	50000	5000000						3	0.256
2020-03-09T04:46:07	mnd9	75211backdoorb	50000	5000000						3	0.256
2020-03-16T21:04:34	Nesowa	6700T	50000	5000000						3	0.256
2020-03-26T07:51:08	kracker	O0	50000	5000000						3	0.256
2020-04-07T05:02:15	daveward2005	Davy	50000	5000000						3	0.256
2020-04-21T00:58:36	mnd9	75211backdoorb	50000	5000000	141623817478505572926989807	86.872	3	2	6487891411068433	3	0.256

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	ANONYMOUS	v4_computers	1FD33D4B5691774E	0.143
2018-04-12T10:14:10	kkmrkkblmbrbk	old	1FD33D4B5691774E	0.143

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-04-21T04:46:01

CrypticClue

cruncher

141623817478505572926989807

BE6CA6DEF28F397D

2020-04-22T06:55:54

atrench

Thinkpad

141623817478505572926989807

BE6CA6DEF28F397D

2020-04-23T13:04:49

arnaud

stm-11-010

141623817478505572926989807

BE6CA6DEF28F397D

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 700000, B2 = 21000000 (P-1 stage 2)

B1 = 700000 (P-1 stage 1)

B1 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 149086 (P-1 stage 1)

B1 = 119543 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 50000 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-04-23T13:04:49+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