M1946621 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	15.2644	68.6567%	500000	15000000	0.1015	5.1064%	15.3658	70.2572%	1.6005%
PrimeNet	2⁵⁸	0.0197	63.7931%	8000	140000	0.0012	2.4659%	0.0209	64.6859%	0.8928%
GPU72	2⁶²	0.3156	66.1290%	8000	90000	0.0010	1.1527%	0.3166	66.5195%	0.3904%
Difference	+5	+14.9488	+2.5277%	+492000	+14910000	+0.1005	+3.9537%	+15.0492	+3.7378%	+3.7378%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.2644

68.6567%

500000

15000000

0.1015

5.1064%

15.3658

70.2572%

1.6005%

PrimeNet

2⁵⁸

0.0197

63.7931%

8000

140000

0.0012

2.4659%

0.0209

64.6859%

0.8928%

GPU72

2⁶²

0.3156

66.1290%

8000

90000

0.0010

1.1527%

0.3166

66.5195%

0.3904%

Difference

+14.9488

+2.5277%

+492000

+14910000

+0.1005

+3.9537%

+15.0492

+3.7378%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1946621	11679727	8	23.478	3 3	-	1	3	5.745e-13	8.723e-8	1.601e-7
1946621	22534084697	11	34.391	5788 2² × 1447	2008-07-15	4	1447	1.473e-9	6.499e-6	1.156e-5
1946621	7033087085445080871097	22	72.575	1806485978894988 2² × 3 × 5223899 × 28817651	2018-05-11	5223899	28817651	541.05	0.5120	0.8363

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1946621

11679727

23.478

3
3

5.745e-13

8.723e-8

1.601e-7

1946621

22534084697

34.391

5788
2² × 1447

2008-07-15

1447

1.473e-9

6.499e-6

1.156e-5

1946621

7033087085445080871097

72.575

1806485978894988
2² × 3 × 5223899 × 28817651

2018-05-11

5223899

28817651

541.05

0.5120

0.8363

exponent	prime factors	composite factor	digits	bits*
1946621	11679727 22534084697	263191957455837719	18	57.869
1946621	11679727 7033087085445080871097	82144537125224218067335150519	29	96.052
1946621	22534084697 7033087085445080871097	158484180064796328291314337302609	33	106.966
1946621	11679727 22534084697 7033087085445080871097	1851051956975663425044927930880389507743	40	130.444

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:19:10	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 11679727 skipped known factor: 22534084697	-	-	0.101	-	-	5.106%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:48:00	J Feitsma	Manual testing	?	?	22534084697	34.391	11	2.97237e-10	0.234	6.58796e-10

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:48:00

J Feitsma

Manual testing

22534084697

34.391

2.97237e-10

0.234

6.58796e-10

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.421 GHz-days
Estimated T-Level:	24.464

Digits	B1	Curves	Complete	FacMiss
20	11000	250 / 100	2.500	8.106%
25	50000	250 / 280	0.893	40.883%

New Calculation Method

Total ECM effort:	20.421 GHz-days
Estimated T-Level:	24.464

Digits	B1	Complete	FacMiss
20	11000	10.313	0.003%
25	50000	0.975	37.719%
30	250000	0.062	93.973%
35	1000000	0.003	99.708%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	1.530
50000	5000000	7033087085445080871097	3	0.209
50000	5990784		14	1.052
50000	7500000		211	17.63

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-08-04T15:39:52	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2018-05-11T06:29:17	ATH	ec2-ECMCF	50000	5000000	7033087085445080871097	72.575	3	2		3	0.209
2020-11-12T11:35:00	nordi	sweet16	50000	5000000						7	0.487
2021-02-21T15:50:09	seatsea	dt	50000	5990784						7	0.526
2021-05-31T09:20:47	MarkS	desktop-i7	50000	5000000						7	0.487
2021-07-14T09:05:48	seatsea	Manual testing	50000	5990784						7	0.526
2021-12-21T23:29:56	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.487
2022-04-14T10:51:23	TJAOI	Manual testing	50000	7500000						211	17.63

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T04:36:44

Oliver Kruse

GTX-1

11679727

22534084697

9D48B4917C59AA__

2017-11-11T09:19:38

kkmrkkblmbrbk

c4.xlarge

11679727

22534084697

9D48B4917C59AA__

2018-05-15T11:17:15

Oliver Kruse

GTX-7

11679727

22534084697

7033087085445080871097

6215DEB18FE52A__

2018-05-15T11:59:52

ATH

ec2-PRPCFDC

11679727

22534084697

7033087085445080871097

6215DEB18FE52A__

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

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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