M1154221 Mersenne number exponent details

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M1154221

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>>>

is 2 ^1154221 - 1

has 347456 decimal digits

takes 0.034 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	C13D96F779F0B12A	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	25.7437	68.6567%	300000	10000000	0.0356	4.1404%	25.7793	69.9545%	1.2977%
PrimeNet	2⁵⁶	0.0083	62.5000%	5000	80000	0.0004	2.2518%	0.0087	63.3444%	0.8444%
GPU72	2⁶⁰	0.1331	65.0000%	5000	26000	0.0003	0.7715%	0.1333	65.2700%	0.2700%
Difference	+7	+25.6106	+3.6567%	+295000	+9974000	+0.0353	+3.3689%	+25.6460	+4.6844%	+4.6844%

Known prime factors (3 factors, 204.9 bits, 0.01775213% 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
1154221	1837195784165694751	19	60.672	795859624875 3 × 5³ × 7 × 31 × 9780149	2007-10-09	125	9780149	0.1421	0.0229	0.0428
1154221	550292418199991571761	21	68.899	238382605324280 2³ × 5 × 414833 × 14366179	2017-07-02	414833	14366179	72.717	0.0505	0.0628
1154221	47417234609458216053281	23	75.328	20540795311061840 2⁴ × 5 × 7919 × 51683 × 627349	2014-12-28	51683	627349	12,771	0.0036	0.0045

4 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1154221	1837195784165694751 550292418199991571761	1010994910775369949685678127309037526511	40	129.571
1154221	1837195784165694751 47417234609458216053281	87114743521292307938971733921156598028031	41	136.00004
1154221	550292418199991571761 47417234609458216053281	26093344697595094660032053948608789310997841	44	144.227
1154221	1837195784165694751 550292418199991571761 47417234609458216053281	47938582873203993100916992327760061218542798459599 592826032591	62	204.899

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-16T00:00:00	Jocelyn Larouche	v4_computers	1000	1000		-		-	-	4.29764e-5	-	-	0.005%
2002-03-24T00:00:00	Jocelyn Larouche	v4_computers	4000	4000		-		-	-	0.000	-	-	0.049%
2002-06-02T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.004	-	-	1.744%
2014-12-28T12:45:00	alpertron	Manual testing	300000	10000000	12		47417234609458216053281	23	75.328	0.036	0.068	0.071	4.140%

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		-	-	0.017	-	-
2003-05-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.033	-	-
2022-04-12T17:43:27	LordJulius	Manual testing	2¹	2⁶¹	1837195784165694751	60.672	19	0.142	0.069	0.289
2022-04-12T17:43:27	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	0.266	-	-
2022-04-12T17:43:27	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.850	-	-
2022-04-12T17:43:27	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	1.701	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.754 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	17.754 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
		1837195784165694751	1	0.00000e+0
50000	5000000		220	7.796
50000	5000000	550292418199991571761	61	2.162
250000	25000000		44	7.796

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-10-09T15:35:00	Team_Bundu	bundu4			1837195784165694751	60.672		1		1	-
2017-06-30T19:48:30	TJAOI	Manual testing	50000	5000000						79	2.800
2017-06-30T19:48:30	TJAOI	Manual testing	50000	5000000	550292418199991571761	68.899	61	2		61	2.162
2018-05-11T11:14:26	TJAOI	Manual testing	50000	5000000						141	4.997
2020-09-25T08:54:22	TJAOI	Manual testing	250000	25000000						44	7.796

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-07-14T00:00:00	ANONYMOUS	v4_computers	C13D96F779F0B12A	0.034

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-29T07:35:33

Oliver Kruse

GTX-1

1837195784165694751

550292418199991571761

47417234609458216053281

E4B3F4E9AA23BBF7

2017-09-30T15:11:55

alpertron

Manual testing

1837195784165694751

550292418199991571761

47417234609458216053281

E4B3F4E9AA23BB__

2017-10-17T07:11:06

Oliver Kruse

Threadripper

1837195784165694751

550292418199991571761

47417234609458216053281

E4B3F4E9AA23BB__

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 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 4000 (P-1 stage 1)

B1 = 1000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-12T17:43:27+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