M2797939 Mersenne number exponent details

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M2797939

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is 2 ^2797939 - 1

has 842264 decimal digits

takes 0.216 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	59649B7745F95556	double-checked
PRP	F9302A19353A56F1	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	21.3031	67.6471%	2700000	84000000	0.7984	7.6900%	22.1016	70.1350%	2.4879%
PrimeNet	2⁵⁹	0.0274	62.7119%	12000	240000	0.0027	2.9267%	0.0302	63.8032%	1.0913%
GPU72	2⁶³	0.5704	65.0794%	15000	260000	0.0032	1.7895%	0.5736	65.7043%	0.6249%
Difference	+5	+20.7327	+2.5677%	+2685000	+83740000	+0.7953	+5.9005%	+21.5280	+4.4307%	+4.4307%

Known prime factors (1 factor, 76.5 bits, 0.00273394% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2797939	106403238699253075214983	24	76.494	19014574424112369 3⁵ × 151 × 1439 × 360116147	2020-10-11	1439	360116147	10,240	2.1975	4.1040

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.243%
2010-11-12T11:43:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.211%
2010-12-21T22:27:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.271%
2011-01-02T14:09:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.374%
2011-01-24T01:10:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.541%
2011-02-18T01:27:00	markr	Manual testing	110000	2310000		-		-	-	0.026	-	-	2.596%
2016-07-24T21:21:51	Jocelyn Larouche	Manual testing	181875	4620000	6	-		-	-	0.047	-	-	3.314%
2016-12-29T21:56:32	Jocelyn Larouche	low 4M	218250	218250		-		-	-	0.024	-	-	1.285%
2017-04-21T13:07:05	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.690%
2017-05-13T16:00:12	Jocelyn Larouche	low 4M	363750	3637500	6	-		-	-	0.061	-	-	3.460%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:22	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.055	-	-
2009-02-13T00:40:00	Sturle Sunde	kraus.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-02-27T21:40:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.110	-	-
2013-01-14T12:31:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.351	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.702	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.335	-	-
2016-02-10T11:15:45	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.671	-	-
2017-10-20T11:26:18	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.342	-	-
2019-02-27T02:18:52	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.68	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.479 GHz-days
Estimated T-Level:	2.150

Digits	B1	Curves	Complete	FacMiss
20	11000	43 / 100	0.430	64.910%
25	50000	43 / 280	0.154	85.740%

New Calculation Method

Total ECM effort:	4.479 GHz-days
Estimated T-Level:	2.150

Digits	B1	Complete	FacMiss
20	11000	1.387	24.980%
25	50000	0.125	88.218%
30	250000	0.008	99.231%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		40	4.167
50000	5000000	106403238699253075214983	3	0.313

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-18T21:51:00	S36049	Wolle3	50000	5000000						3	0.313
2011-02-20T15:51:00	Richard Kint	Desktop	50000	5000000						3	0.313
2013-03-21T03:25:00	Donna Noble	PH2x6	50000	5000000						3	0.313
2015-03-22T08:48:00	Jason U	Server7	50000	5000000						3	0.313
2016-02-17T00:12:29	Sintax	cloud	50000	5000000						3	0.313
2016-05-29T04:49:56	Jason U	Server7	50000	5000000						3	0.313
2017-02-11T03:48:30	Bruce	eleven	50000	5000000						3	0.313
2017-08-22T08:57:16	JMGarcia	jmgarcia-pW07	50000	5000000						3	0.313
2018-01-29T13:02:58	Angel Pescador		50000	5000000						3	0.313
2018-11-28T14:26:37	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2020-08-15T22:22:49	daveward2005	Dave2	50000	5000000						3	0.313
2020-09-13T14:15:54	mat10243x	K3	50000	5000000						7	0.729
2020-10-11T21:53:03	mnd9	75204	50000	5000000	106403238699253075214983	76.494	3	2	4242700160016572	3	0.313

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	ANONYMOUS	v4_computers	59649B7745F95556	0.216
2018-08-31T13:53:07	kkmrkkblmbrbk	old	59649B7745F95556	0.216

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-10-12T15:38:31

mrh.org

106403238699253075214983

F9302A19353A56F1

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 = 2700000, B2 = 84000000 (P-1 stage 2)

B1 = 2700000 (P-1 stage 1)

B1 = 363750, B2 = 3637500 (P-1 stage 2)

B1 = 181875, B2 = 4620000 (P-1 stage 2)

B1 = 363750 (P-1 stage 1)

B1 = 110000, B2 = 2310000 (P-1 stage 2)

B1 = 218250 (P-1 stage 1)

B1 = 181875 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (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

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-10-12T15:38:31+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