M1940971 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	Prob over default TF
Actual	2⁶⁷	15.3088	68.6567%	500000	15000000	0.1015	5.1046%	15.4103	70.2567%	1.6000%
PrimeNet	2⁵⁸	0.0198	63.7931%	8000	140000	0.0012	2.4645%	0.0210	64.6854%	0.8923%
GPU72	2⁶²	0.3165	66.1290%	8000	90000	0.0010	1.1520%	0.3175	66.5192%	0.3902%
Difference	+5	+14.9923	+2.5277%	+492000	+14910000	+0.1005	+3.9527%	+15.0928	+3.7375%	+3.7375%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.3088

68.6567%

500000

15000000

0.1015

5.1046%

15.4103

70.2567%

1.6000%

PrimeNet

2⁵⁸

0.0198

63.7931%

8000

140000

0.0012

2.4645%

0.0210

64.6854%

0.8923%

GPU72

2⁶²

0.3165

66.1290%

8000

90000

0.0010

1.1520%

0.3175

66.5192%

0.3902%

Difference

+14.9923

+2.5277%

+492000

+14910000

+0.1005

+3.9527%

+15.0928

+3.7375%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1940971	3156018847	10	31.555	813 3 × 271	-	3	271	1.733e-10	1.385e-6	2.203e-6
1940971	8152078201	10	32.925	2100 2² × 3 × 5² × 7	2008-07-15	25	25	4.288e-10	1.967e-6	4.002e-6
1940971	970694352361543	15	49.786	250053801 3 × 83351267	2008-08-26	3	83351267	4.634e-5	0.3572	0.6672
1940971	607348233079068791	18	59.075	156454741745 5 × 31290948349	2015-10-23	5	31290948349	0.0679	134.11	250.47
1940971	810612319674307462199	21	69.458	208816185217169 208816185217169	2020-11-02	1	208816185217169	96.295	894,934	1,671,487

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1940971

3156018847

31.555

813
3 × 271

271

1.733e-10

1.385e-6

2.203e-6

1940971

8152078201

32.925

2100
2² × 3 × 5² × 7

2008-07-15

4.288e-10

1.967e-6

4.002e-6

1940971

970694352361543

49.786

250053801
3 × 83351267

2008-08-26

83351267

4.634e-5

0.3572

0.6672

1940971

607348233079068791

59.075

156454741745
5 × 31290948349

2015-10-23

31290948349

0.0679

134.11

250.47

1940971

810612319674307462199

69.458

208816185217169
208816185217169

2020-11-02

208816185217169

96.295

894,934

1,671,487

exponent	prime factors	composite factor	digits	bits*
1940971	3156018847 8152078201	25728112444573854247	20	64.480
1940971	3156018847 970694352361543	3063529670729488666000921	25	81.341
1940971	8152078201 970694352361543	7913176269720347561024143	25	82.711
1940971	3156018847 607348233079068791	1916802470289689945605503977	28	90.631
1940971	8152078201 607348233079068791	4951150291299743800490524991	28	92.000
1940971	3156018847 810612319674307462199	2558307758502503252372784064553	31	101.013
1940971	8152078201 810612319674307462199	6608175020678965282364099423999	31	102.382
1940971	970694352361543 607348233079068791	589549499766614147075274199904513	33	108.861
1940971	3156018847 8152078201 970694352361543	24974133446870572321982677930023121	35	114.266
1940971	970694352361543 810612319674307462199	786856800662539942960030942853813057	36	119.244
1940971	3156018847 8152078201 607348233079068791	15625923633671531560619504716520505377	38	123.555
1940971	607348233079068791 810612319674307462199	492323960066315908751629949165353131409	39	128.533
1940971	3156018847 8152078201 810612319674307462199	20855524909537429167599774498322688109153	41	133.938
1940971	3156018847 970694352361543 607348233079068791	1860629332502856349546395302591488628356511	43	140.417
1940971	8152078201 970694352361543 607348233079068791	4806053625457869775950550711139296708821113	43	141.786
1940971	3156018847 970694352361543 810612319674307462199	2483334892781098146872162623349813973706685279	46	150.799
1940971	8152078201 970694352361543 810612319674307462199	6414518171989694226296251663524046151698870457	46	152.168
1940971	3156018847 607348233079068791 810612319674307462199	1553783696798968377876076361535506402137271665423	49	160.088
1940971	8152078201 607348233079068791 810612319674307462199	4013463422686608434113667631809613407026397315209	49	161.457
1940971	3156018847 8152078201 970694352361543 607348233079068791	15167995821637716017371605384384873255364503779516 711	53	173.341
1940971	970694352361543 607348233079068791 810612319674307462199	47789608756864267956721061504664594545531936915700 4087	54	178.319
1940971	3156018847 8152078201 970694352361543 810612319674307462199	20244340245223462467958053255536992092459456230903 503079	56	183.724
1940971	3156018847 8152078201 607348233079068791 810612319674307462199	12666566203744063592571892786284996628359192153309 803744023	59	193.013
1940971	3156018847 970694352361543 607348233079068791 810612319674307462199	15082490592741987029226985043056763879931219254636 55400628027689	64	209.874
1940971	8152078201 970694352361543 607348233079068791 810612319674307462199	38958462778115190792580857692975650101113440487978 84764100607487	64	211.243
1940971	3156018847 8152078201 970694352361543 607348233079068791 810612319674307462199	12295364277787952127838605465045609123119147386507 412009235666233121307489	74	242.799

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:41:54	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 3156018847 skipped known factor: 8152078201	-	-	0.101	-	-	5.105%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:41:54

alpertron

Manual testing

500000

15000000

skipped known factor: 3156018847
skipped known factor: 8152078201

0.101

-

-

5.105%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T20:20:00	ANONYMOUS	Manual testing	?	?	970694352361543	49.786	15	7.70251e-6	0.233	1.70752e-5
2008-07-15T07:48:00	J Feitsma	Manual testing	?	?	8152078201	32.925	10	1.33993e-10	0.234	2.97139e-10
2015-10-23T11:16:01	TJAOI	Manual testing	2⁵⁹	2⁶⁰*	607348233079068791	59.075	18	0.028	0.214	0.057

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-08-26T20:20:00

ANONYMOUS

Manual testing

970694352361543

49.786

7.70251e-6

0.233

1.70752e-5

2008-07-15T07:48:00

J Feitsma

Manual testing

8152078201

32.925

1.33993e-10

0.234

2.97139e-10

2015-10-23T11:16:01

TJAOI

Manual testing

2⁵⁹

2⁶⁰*

607348233079068791

59.075

0.028

0.214

0.057

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.856 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	19.856 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.799	0.015%
25	50000	0.797	45.067%
30	250000	0.049	95.190%
35	1000000	0.002	99.774%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	2.712
50000	5000000	810612319674307462199	5	0.348
50000	6600000		214	16.80

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

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-04-26T04:50:52	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2018-05-08T18:05:59	ATH	ec2-ECMCF	50000	5000000						3	0.209
2020-11-02T23:04:54	nordi	sweet16	50000	5000000	810612319674307462199	69.458	5	2	3572922006607407	5	0.348
2021-01-17T13:08:17	Kublenz	Medion_E4272	50000	5000000						7	0.487
2021-04-16T12:20:29	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.487
2021-07-26T10:56:52	volki	home	50000	5000000						7	0.487
2021-10-14T16:50:10	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.487
2022-03-04T23:42:00	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.487
2022-04-21T11:52:19	TJAOI	Manual testing	50000	6600000						214	16.80