M632 683 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown	2000000	6199753560	7.4836	46.4081%	7.4836	46.4081%
Target	2⁴⁴	0.0000	54.5455%	11000	400000	0.0007	15.9081%	0.0007	61.7764%
Difference	-44	0.0000	-54.5455%	+1989000	+6199353560	+7.4829	+30.5000%	+7.4829	-15.3683%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

unknown

2000000

6199753560

7.4836

46.4081%

7.4836

46.4081%

Target

2⁴⁴

0.0000

54.5455%

11000

400000

0.0007

15.9081%

0.0007

61.7764%

Difference

-44

0.0000

-54.5455%

+1989000

+6199353560

+7.4829

+30.5000%

+7.4829

-15.3683%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
632683	105674510759	12	36.621	83513 23 × 3631	-	23	3631	1.558e-8	4.838e-6	8.150e-6
632683	3768712691278316481200916553	28	91.606	2978357796304244369772 2² × 3 × 17 × 41 × 113 × 3931 × 18461 × 43423631	2023-01-13	18461	43423631	856,458,220	0.0525	0.0974

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

632683

105674510759

36.621

83513
23 × 3631

3631

1.558e-8

4.838e-6

8.150e-6

632683

3768712691278316481200916553

91.606

2978357796304244369772
2² × 3 × 17 × 41 × 113 × 3931 × 18461 × 43423631

2023-01-13

18461

43423631

856,458,220

0.0525

0.0974

exponent	prime factors	composite factor	digits	bits*
632683	105674510759 3768712691278316481200916553	398256869842070300456073277520659693727	39	128.227

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17	alpertron	Manual testing	1000000	30000000	12	-	skipped known factor: 105674510759	-	-	0.057	-	-	31.566%
2023-01-15	USAFSS	USAFSACS	2000000	6199753560			3768712691278316481200916553	28	91.606	7.484	0.019	14.97	46.408%

ECM factoring results:

Total ECM effort:	18.813 GHz-days
Estimated T-Level:	26.530

Digits	B1	Complete	FacMiss
20	11000	24.808	0.000%
25	50000	3.182	4.149%
30	250000	0.306	73.637%
35	1000000	0.023	97.679%
40	3000000	0.002	99.849%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	4.780
250000	25000000		44	3.743
250000	40000000		42	4.322
250000	40000000	3768712691278316481200916553	58	5.968

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-01-18	Richard B. Woods	Puttputt	50000	5000000						1	0.017
2015-09-04	TJAOI	Manual testing	50000	5000000						99	1.684
2016-04-15	TJAOI	Manual testing	50000	5000000						90	1.531
2016-11-25	TJAOI	Manual testing	50000	5000000						91	1.548
2019-02-15	TJAOI	Manual testing	250000	25000000						44	3.743
2023-01-04	TJAOI	Manual testing	250000	40000000	3768712691278316481200916553	91.606	58	2	1519468026266927	58	5.968
2023-01-04	TJAOI	Manual testing	250000	40000000						42	4.322

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-3

105674510759

432E04D365C48A__

2017-09-28

Oliver Kruse

Manual testing

105674510759

432E04D365C48A__

2017-11-09

kkmrkkblmbrbk

c4.large

105674510759

432E04D365C48A__

2020-04-19

Oliver Kruse

AddPrpType5

105674510759

23471C013BFD10__

2023-01-13

Naegi Makoto

5950X

105674510759

3768712691278316481200916553

23471C013BFD1027

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 = 2000000, B2 = 6199753560 (P-1 stage 2)

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

B1 = 2000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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