M751 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

738D91D23C73EC33

PRP-tested

Cofactor is a certified prime

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	39,565.8023	85.0746%	3000000000	4290000000	0.0587	9.5656%	39,565.8611	86.5023%
Target	2⁴⁴	0.0031	77.2727%	500	50000	0.0000	0.5505%	0.0031	77.3978%
Difference	+23	+39,565.7992	+7.8019%	+2999999500	+4289950000	+0.0587	+9.0151%	+39,565.8579	+9.1045%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁶⁷

39,565.8023

85.0746%

3000000000

4290000000

0.0587

9.5656%

39,565.8611

86.5023%

Target

2⁴⁴

0.0031

77.2727%

500

50000

0.0000

0.5505%

0.0031

77.3978%

Difference

+23

+39,565.7992

+7.8019%

+2999999500

+4289950000

+0.0587

+9.0151%

+39,565.8579

+9.1045%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
751	22764024512532445092774588186840266769462045797638 1782672549806487	66	217.112	15155808596892440141660844332117354706699098400558 0414562283493 3² × 294641 × 57153577845175956660104422112625023924403288523842165197	-	294641	57153577845175956660104422112625023924403288523842165197	2.282e+14	5.957e+43	1.113e+44
751	64935003199370114500077042183338517573218246028593 05748523089149897	67	221.946	43232358987596614181143170561477042325711215731420 14479709113948 2² × 3 × 7 × 17² × 647 × 38273 × 257021957 × 2537261620168202723 × 11028070721134373040809603	-	2537261620168202723	11028070721134373040809603	2.362e+14	1.150e+13	2.147e+13
751	hide decimal representation P94 click to show decimal representation	94	311.942

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

751

22764024512532445092774588186840266769462045797638
1782672549806487

217.112

15155808596892440141660844332117354706699098400558
0414562283493
3² × 294641 × 57153577845175956660104422112625023924403288523842165197

294641

57153577845175956660104422112625023924403288523842165197

2.282e+14

5.957e+43

1.113e+44

751

64935003199370114500077042183338517573218246028593
05748523089149897

221.946

43232358987596614181143170561477042325711215731420
14479709113948
2² × 3 × 7 × 17² × 647 × 38273 × 257021957 × 2537261620168202723 × 11028070721134373040809603

2537261620168202723

11028070721134373040809603

2.362e+14

1.150e+13

2.147e+13

751

P94

click to show decimal representation

311.942

exponent	prime factors	composite factor	digits	bits*
751	22764024512532445092774588186840266769462045797638 1782672549806487 64935003199370114500077042183338517573218246028593 05748523089149897	14781820045518340332428072154976870854594477724360 22889725172760272703941316610709797869969027502099 712795003306668270268676685981839	133	439.058

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-02-04	ANONYMOUS	v4_computers	1000000	100000000		-		-	-	0.000	-	-	3.042%
2001-02-11	ANONYMOUS	v4_computers	1000000	100000000		-		-	-	0.000	-	-	3.042%
2001-02-11	ANONYMOUS	v4_computers	10000000	1000000000		-		-	-	0.001	-	-	6.059%
2001-05-13	ANONYMOUS	v4_computers	3000000000	4290000000		-		-	-	0.059	-	-	9.566%
2002-01-02	ANONYMOUS	v4_computers	16777216	1677721600		-		-	-	0.002	-	-	6.857%
2002-01-02	ANONYMOUS	v4_computers	33554432	3355443200		-		-	-	0.004	-	-	7.987%
2002-01-02	ANONYMOUS	v4_computers	67108864	4290000000		-		-	-	0.006	-	-	8.668%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-05	ANONYMOUS	v4_computers	2⁵¹	2⁵³		-	-	1.198	-	-
1998-08-16	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	1.598	-	-
2000-01-12	ANONYMOUS	v4_computers	2⁵⁴	2⁵⁵		-	-	3.196	-	-
2000-06-28	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	12.78	-	-
2001-05-20	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	25.56	-	-

date	userid	compid	cofactors	res64	PRP
2018-01-24	Luke_Richards	work-laptop		738D91D23C73EC33	no

date

userid

compid

cofactors

res64

PRP

2018-01-24

Luke_Richards

work-laptop

738D91D23C73EC33

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 = 3000000000, B2 = 4290000000 (P-1 stage 2)

B1 = 3000000000 (P-1 stage 1)

B1 = 67108864, B2 = 4290000000 (P-1 stage 2)

B1 = 33554432, B2 = 3355443200 (P-1 stage 2)

B1 = 16777216, B2 = 1677721600 (P-1 stage 2)

B1 = 67108864 (P-1 stage 1)

B1 = 10000000, B2 = 1000000000 (P-1 stage 2)

B1 = 33554432 (P-1 stage 1)

B1 = 16777216 (P-1 stage 1)

B1 = 10000000 (P-1 stage 1)

B1 = 1000000, B2 = 100000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

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TF factor-bounds graph:

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2⁵³

this exponent TF target: 44

TF double-checked to: 67.9

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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