M1901839 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	15.6238	68.6567%	2000000	262000000	1.2716	9.2335%	16.8954	71.5508%	2.8941%
PrimeNet	2⁵⁷	0.0101	63.1579%	9000	160000	0.0014	3.0386%	0.0114	64.2774%	1.1195%
GPU72	2⁶¹	0.1615	65.5738%	10000	160000	0.0014	1.7277%	0.1629	66.1685%	0.5948%
Difference	+6	+15.4623	+3.0829%	+1990000	+261840000	+1.2702	+7.5059%	+16.7325	+5.3823%	+5.3823%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.6238

68.6567%

2000000

262000000

1.2716

9.2335%

16.8954

71.5508%

2.8941%

PrimeNet

2⁵⁷

0.0101

63.1579%

9000

160000

0.0014

3.0386%

0.0114

64.2774%

1.1195%

GPU72

2⁶¹

0.1615

65.5738%

10000

160000

0.0014

1.7277%

0.1629

66.1685%

0.5948%

Difference

+15.4623

+3.0829%

+1990000

+261840000

+1.2702

+7.5059%

+16.7325

+5.3823%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1901839	304294241	9	28.181	80 2⁴ × 5	-	16	16	1.913e-11	1.259e-6	2.561e-6
1901839	2620488368867501201	19	61.185	688935385400 2³ × 5² × 29 × 118781963	2016-04-07	29	118781963	0.2084	0.5091	0.9508
1901839	6240910991184829939633	22	72.402	1640756917695144 2³ × 3 × 27847 × 2455017473	2021-04-03	27847	2455017473	655.69	10.524	19.651

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1901839

304294241

28.181

80
2⁴ × 5

1.913e-11

1.259e-6

2.561e-6

1901839

2620488368867501201

61.185

688935385400
2³ × 5² × 29 × 118781963

2016-04-07

118781963

0.2084

0.5091

0.9508

1901839

6240910991184829939633

72.402

1640756917695144
2³ × 3 × 27847 × 2455017473

2021-04-03

27847

2455017473

655.69

10.524

19.651

exponent	prime factors	composite factor	digits	bits*
1901839	304294241 2620488368867501201	797399519253864307524883441	27	89.365
1901839	304294241 6240910991184829939633	1899073273211145517194699553553	31	100.583
1901839	2620488368867501201 6240910991184829939633	16354234663537195175053359074556384999233	41	133.587
1901839	304294241 2620488368867501201 6240910991184829939633	4976499424076941181061724034092597585045391317153	49	161.768

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:40:45	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 304294241	-	-	0.101	-	-	5.092%
2021-04-06T23:08:45	Dylan Delgado	desktoplinux	1000000	71000000		-	skipped known factor: 304294241	-	-	0.379	-	-	7.162%
2021-06-29T23:13:41	Dylan Delgado	laptop-i78750	2000000	262000000		-	skipped known factor: 304294241 skipped known factor: 2620488368867501201	-	-	1.272	-	-	9.234%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2016-04-07T11:48:39	TJAOI	Manual testing	2⁶¹	2⁶²*	2620488368867501201	61.185	19	0.047	0.210	0.095

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2016-04-07T11:48:39

TJAOI

Manual testing

2⁶¹

2⁶²*

2620488368867501201

61.185

0.047

0.210

0.095

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.385 GHz-days
Estimated T-Level:	24.732

Digits	B1	Curves	Complete	FacMiss
20	11000	265 / 100	2.650	6.972%
25	50000	265 / 280	0.946	38.747%

New Calculation Method

Total ECM effort:	20.385 GHz-days
Estimated T-Level:	24.732

Digits	B1	Complete	FacMiss
20	11000	9.049	0.012%
25	50000	0.820	44.054%
30	250000	0.051	95.055%
35	1000000	0.002	99.767%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		35	2.428
50000	5000000	6240910991184829939633	5	0.347
50000	6600000		225	17.61

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-11-13T00:28:20	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-27T01:19:09	alpertron		50000	5000000						3	0.208
2018-09-28T16:58:09	alpertron	Manual testing	50000	5000000						3	0.208
2020-10-17T21:59:34	MarkS	laptop64	50000	5000000						7	0.486
2021-01-09T02:24:11	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.486
2021-04-03T17:47:50	MarkS	desktop-i7	50000	5000000	6240910991184829939633	72.402	5	2	2658157696945284	5	0.347
2021-12-11T06:31:32	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.486
2021-12-13T10:01:58	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.486
2021-12-17T10:36:36	TJAOI	Manual testing	50000	6600000						225	17.61

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T19:04:07

Oliver Kruse

GTX-0

304294241

2620488368867501201

400275BA021541__

2017-11-09T09:03:46

ATH

ec2-1xf

304294241

2620488368867501201

400275BA021541__

2021-04-05T12:54:31

daveward2005

Davy

304294241

2620488368867501201

6240910991184829939633

840516328A7BAE32

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 = 262000000 (P-1 stage 2)

B1 = 1000000, B2 = 71000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (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