M1905437 Mersenne number exponent details

is 2 ^1905437 - 1

has 573594 decimal digits

takes 0.103 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	31.2815	69.1176%	8000000	320000000	1.9665	9.7332%	33.2479	72.1235%	3.0058%
PrimeNet	2⁵⁷	0.0101	63.1579%	9000	160000	0.0014	3.0396%	0.0114	64.2778%	1.1199%
GPU72	2⁶¹	0.1612	65.5738%	10000	160000	0.0014	1.7283%	0.1626	66.1688%	0.5950%
Difference	+7	+31.1203	+3.5439%	+7990000	+319840000	+1.9650	+8.0048%	+33.0853	+5.9547%	+5.9547%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1905437	396012414245897988590209	24	78.390	103916428159497792 2⁶ × 3 × 233 × 2322881530747	2020-01-18	233	2322881530747	53,490	9,955.3	18,594

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-06-09T01:34:00	kurly	slice	1000000	30000000		-		-	-	0.203	-	-	5.681%
2017-11-27T11:41:02	mikr	S061	8000000	320000000	12	-		-	-	1.966	-	-	9.733%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2¹	2⁵⁶		-	-	0.005	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁶	2⁵⁷		-	-	0.005	-	-
2002-01-02T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁷	2⁵⁸		-	-	0.010	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁸	2⁵⁹		-	-	0.020	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁹	2⁶⁰		-	-	0.040	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁶⁰	2⁶¹		-	-	0.081	-	-
2009-05-25T12:15:00	Architects Cubed	i4l_1	2⁶⁰	2⁶¹		-	-	0.081	-	-
2011-02-07T07:13:00	GrunwalderGIMP	GWPrime02	2⁶¹	2⁶²		-	-	0.161	-	-
2011-02-07T07:13:00	GrunwalderGIMP	GWPrime02	2⁶²	2⁶³		-	-	0.515	-	-
2015-05-17T05:14:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.030	-	-
2015-05-19T06:11:00	omylist	Manual testing	2⁶⁴	2⁶⁵		-	-	1.961	-	-
2015-08-31T08:30:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.922	-	-
2017-03-15T08:26:27	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	7.844	-	-
2019-04-26T04:32:10	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	15.69	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.956 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	18.956 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.482	0.021%
25	50000	0.768	46.393%
30	250000	0.047	95.364%
35	1000000	0.002	99.782%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		75	5.204
50000	5000000	396012414245897988590209	3	0.208
50000	6600000		173	13.54

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-04T04:22:00	Hoang Anh Vo	whiterose	50000	5000000						3	0.208
2009-07-29T09:21:00	SubPrime	mysql0	50000	5000000						3	0.208
2010-11-27T01:13:00	James Hintz	ryan	50000	5000000						3	0.208
2012-10-18T01:39:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.208
2013-11-20T08:12:00	OS1	L3	50000	5000000						3	0.208
2014-08-08T08:09:00	Sara	Sara	50000	5000000						3	0.208
2015-07-17T15:08:00	Sara	Sara	50000	5000000						3	0.208
2016-01-05T17:47:56	Sara	Sara	50000	5000000						3	0.208
2016-06-12T17:57:56	Bruce	Desk6	50000	5000000						3	0.208
2016-08-19T02:45:26	Bruce	test	50000	5000000						3	0.208
2017-02-03T17:32:49	Bruce	Desk6	50000	5000000						3	0.208
2017-07-18T19:46:32	Bruce	Desk6	50000	5000000						3	0.208
2017-12-04T11:43:40	Bruce	Desk6	50000	5000000						3	0.208
2018-04-03T17:56:11	Bruce	Desk6	50000	5000000						3	0.208
2018-09-07T20:39:30	Bruce	Desk6	50000	5000000						3	0.208
2019-11-27T07:03:36	wazuma	G751	50000	5000000						3	0.208
2019-11-30T15:56:55	George Woltman	colab	50000	5000000						3	0.208
2019-12-04T05:49:03	Nesowa	6700T	50000	5000000						3	0.208
2019-12-08T19:59:52	Alvin Bunk	BADCAT	50000	5000000						3	0.208
2019-12-13T18:45:09	cappy95833	HomePC	50000	5000000						3	0.208
2019-12-18T03:29:49	IanGlencross	glenx24	50000	5000000						3	0.208
2019-12-24T03:29:25	IanGlencross	glenx24	50000	5000000						3	0.208
2019-12-29T20:42:31	MarkS	desktop-i7	50000	5000000						3	0.208
2020-01-03T18:11:46	J.R. Allen	lapacer	50000	5000000						3	0.208
2020-01-10T11:58:24	mnd9	25836b	50000	5000000						3	0.208
2020-01-18T08:17:55	daveward2005	Davy	50000	5000000	396012414245897988590209	78.390	3	2		3	0.208
2022-01-18T14:07:39	TJAOI	Manual testing	50000	6600000						173	13.54

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	B95CDB64925FAA15	0.103
2015-07-14T15:04:00	MadPoo	Manual testing	B95CDB64925FAA15	0.103

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-01-23T15:33:26

mnd9

75211backdoor

396012414245897988590209

B3BD0D363F685AA7

2020-02-06T00:00:20

mnd9

f3b

396012414245897988590209

B3BD0D363F685AA7

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 = 8000000, B2 = 320000000 (P-1 stage 2)

B1 = 8000000 (P-1 stage 1)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-18T14:07:39+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