M1 964 659 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	2⁶⁷	15.1242	68.6567%	650000	730452492	3.1789	9.3233%	18.3031	71.5789%
Target	2⁶²	0.3127	66.1290%	8000	720000	0.0037	1.1550%	0.3164	66.5202%
Difference	+5	+14.8115	+2.5277%	+642000	+729732492	+3.1752	+8.1684%	+17.9867	+5.0587%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁶⁷

15.1242

68.6567%

650000

730452492

3.1789

9.3233%

18.3031

71.5789%

Target

2⁶²

0.3127

66.1290%

8000

720000

0.0037

1.1550%

0.3164

66.5202%

Difference

+14.8115

+2.5277%

+642000

+729732492

+3.1752

+8.1684%

+17.9867

+5.0587%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1964659	113950223	9	26.764	29 29	-	1	29	4.579e-12	1.987e-7	1.987e-7
1964659	2142201304513	13	40.962	545184 2⁵ × 3³ × 631	2008-07-15	32	631	7.494e-8	5.084e-6	5.123e-6
1964659	2871582950246945708021469878076620907631	40	131.077	730809506954373687245845176714285 3 × 5 × 7³ × 11 × 619 × 1913 × 10453 × 16339 × 418961 × 152398427	2022-10-31	418961	152398427	8.985e+10	0.6843	1.2199

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1964659

113950223

26.764

29
29

4.579e-12

1.987e-7

1964659

2142201304513

40.962

545184
2⁵ × 3³ × 631

2008-07-15

631

7.494e-8

5.084e-6

5.123e-6

1964659

2871582950246945708021469878076620907631

131.077

730809506954373687245845176714285
3 × 5 × 7³ × 11 × 619 × 1913 × 10453 × 16339 × 418961 × 152398427

2022-10-31

418961

152398427

8.985e+10

0.6843

1.2199

exponent	prime factors	composite factor	digits	bits*
1964659	113950223 2142201304513	244104316360147256399	21	67.726
1964659	113950223 2871582950246945708021469878076620907631	327217517543637368497939381394613763511014851713	48	157.841
1964659	2142201304513 2871582950246945708021469878076620907631	61515087420362962712174791810274723676940982764387 03	52	172.039
1964659	113950223 2142201304513 2871582950246945708021469878076620907631	70096579294148543419930023417593784542508049438410 5852680769	60	198.803

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-08-12	harlee	i5-5250U_1600	132000	134381520		-	skipped known factor: 113950223 skipped known factor: 2142201304513	-	-	0.586	-	-	5.863%
2022-10-31	harlee	i5-5250U_1600	650000	730452492			2871582950246945708021469878076620907631	40	131.077	3.179	0.213	6.358	9.323%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15	J Feitsma	Manual testing	?	?	2142201304513	40.962	13	3.87298e-10	0.527	1.91446e-9

ECM factoring results:

Total ECM effort:	20.969 GHz-days
Estimated T-Level:	25.319

Digits	B1	Complete	FacMiss
20	11000	10.613	0.002%
25	50000	1.002	36.697%
30	250000	0.064	93.811%
35	1000000	0.003	99.700%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	39	2.716
50000	5700000	7	0.515
50000	7500000	212	17.74

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-05-10	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2018-05-23	Michel Thull	MT-Thinkpad	50000	5000000						3	0.209
2021-01-01	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.487
2021-03-29	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.487
2021-07-13	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.487
2021-09-27	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.487
2022-02-04	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.487
2022-05-26	Eric	miniPCWindows	50000	5700000						7	0.515
2022-06-08	TJAOI	Manual testing	50000	7500000						212	17.74

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05

Oliver Kruse

GTX-0

113950223

2142201304513

504FEFA7102AE7__

2017-11-11

ATH

ec2-1xf

113950223

2142201304513

504FEFA7102AE7__

2022-10-31

Kevin_9611

PRP-CF

113950223

2142201304513

2871582950246945708021469878076620907631

A48CAB7156E3A652

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 = 650000, B2 = 730452492 (P-1 stage 2)

B1 = 132000, B2 = 134381520 (P-1 stage 2)

B1 = 650000 (P-1 stage 1)

B1 = 132000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

this exponent TF target: 62

TF double-checked to: 67.9

ECM T-Level=25.32 ~= 67-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

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