M2 251 Mersenne number exponent details

is 2 ²²⁵¹ - 1

has 678 decimal digits

takes 0.000 GHz-days to do one PRP test

Has been fully factored.

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	13,200.3188	82.0896%	-	-	-	-	13,200.3188	82.0896%
Target	2⁴⁴	0.0010	72.7273%	500	80000	0.0000	0.7899%	0.0010	72.9427%
Difference	+23	+13,200.3177	+9.3623%	-500	-80000	0.0000	-0.7899%	+13,200.3177	+9.1468%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2251	400679	6	18.612	89 89	-	1	89	1.581e-11	2.395e-10	3.567e-10
2251	778847	6	19.571	173 173	2009-01-21	1	173	3.219e-11	4.286e-10	7.412e-10
2251	17620954939878356226435007	26	83.865	3914028196330154648253 3 × 1304676065443384882751	2009-01-21	3	1304676065443384882751	1.329e+9	2.937e+9	5.486e+9
2251	1687942505818611032423917201	28	90.447	374931698315995342608600 2³ × 3 × 5² × 624886163859992237681	2009-01-21	25	624886163859992237681	1.201e+11	1.407e+9	2.628e+9
2251	hide decimal representation P614 click to show decimal representation	614	2,038.504		2009-01-21

click to show decimal representation

exponent	prime factors	composite factor	digits	bits*
2251	400679 778847	312067637113	12	38.183
2251	400679 17620954939878356226435007	7060346604355519894451752169753	31	102.478
2251	778847 17620954939878356226435007	13724027892059438111890225896929	32	103.436
2251	400679 1687942505818611032423917201	676323115288895249860582720179479	33	109.059
2251	778847 1687942505818611032423917201	1314648956829307746770270640247247	34	110.018
2251	400679 778847 17620954939878356226435007	5498929771762483603234063822155614791	37	122.049
2251	400679 778847 1687942505818611032423917201	526752229373410198668165269863626680713	39	128.630
2251	17620954939878356226435007 1687942505818611032423917201	29743158836135105119760197977318477813188474375855 407	53	174.313
2251	400679 17620954939878356226435007 1687942505818611032423917201	11917459139303777784280396365353990371710544724443 368621353	59	192.925
2251	778847 17620954939878356226435007 1687942505818611032423917201	23165370030047318217209870914040564489368403702211 856175729	59	193.884
2251	400679 778847 17620954939878356226435007 1687942505818611032423917201	92818772982693294159534338679668593390356426269985 44320634919991	64	212.496

P-1 results:
No P-1 results for M2251

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-01-21	ANONYMOUS	Manual testing	?	?	778847	19.571	6	1.16188e-12	0.001	1.88591e-8

ECM factoring results:

Total ECM effort:

0.000 GHz-days

Digits	B1	Complete	FacMiss

ECM Summary

B1	B2	factor	curves	GHz-days
		17620954939878356226435007	1	0.00000e+0
		1687942505818611032423917201	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-21	ANONYMOUS	Manual testing			17620954939878356226435007	83.865		1		1	-
2009-01-21	ANONYMOUS	Manual testing			1687942505818611032423917201	90.447		1		1	-

Lucas-Lehmer results:
No L-L results for M2251

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-09

kkmrkkblmbrbk

c4.large

400679

778847

17620954939878356226435007

1687942505818611032423917201

PRP

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

10⁰

10¹

10²

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2023-07-11T14:45:05+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