M1853801 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	16.0286	68.6567%	500000	15000000	0.1015	5.0765%	16.1301	70.2478%	1.5911%
PrimeNet	2⁵⁷	0.0104	63.1579%	9000	160000	0.0014	3.0242%	0.0117	64.2721%	1.1142%
GPU72	2⁶¹	0.1657	65.5738%	9000	150000	0.0013	1.6316%	0.1670	66.1355%	0.5617%
Difference	+6	+15.8629	+3.0829%	+491000	+14850000	+0.1002	+3.4448%	+15.9631	+4.1124%	+4.1124%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.0286

68.6567%

500000

15000000

0.1015

5.0765%

16.1301

70.2478%

1.5911%

PrimeNet

2⁵⁷

0.0104

63.1579%

9000

160000

0.0014

3.0242%

0.0117

64.2721%

1.1142%

GPU72

2⁶¹

0.1657

65.5738%

9000

150000

0.0013

1.6316%

0.1670

66.1355%

0.5617%

Difference

+15.8629

+3.0829%

+491000

+14850000

+0.1002

+3.4448%

+15.9631

+4.1124%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1853801	11122807	8	23.407	3 3	-	1	3	6.032e-13	8.723e-8	1.601e-7
1853801	22036740740790156497	20	64.257	5943664055848 2³ × 19² × 1153 × 1784957	2015-07-07	1153	1784957	2.7175	0.0077	0.0143
1853801	272057955679353506441	21	67.882	73378414317220 2² × 5 × 59 × 173137 × 359167	2015-07-07	173137	359167	27.895	0.0144	0.0277
1853801	663188023396082673867361	24	79.134	178872495860149680 2⁴ × 3 × 5 × 43 × 17332606187999	2020-11-21	43	17332606187999	121,796	74,283	138,740

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1853801

11122807

23.407

3
3

6.032e-13

8.723e-8

1.601e-7

1853801

22036740740790156497

64.257

5943664055848
2³ × 19² × 1153 × 1784957

2015-07-07

1153

1784957

2.7175

0.0077

0.0143

1853801

272057955679353506441

67.882

73378414317220
2² × 5 × 59 × 173137 × 359167

2015-07-07

173137

359167

27.895

0.0144

0.0277

1853801

663188023396082673867361

79.134

178872495860149680
2⁴ × 3 × 5 × 43 × 17332606187999

2020-11-21

17332606187999

121,796

74,283

138,740

exponent	prime factors	composite factor	digits	bits*
1853801	11122807 22036740740790156497	245110414168845938215927079	27	87.664
1853801	11122807 272057955679353506441	3026048133836002936916499887	28	91.289
1853801	11122807 663188023396082673867361	7376512388946112137470600002327	31	102.541
1853801	22036740740790156497 272057955679353506441	5995270635775292153490816328214087497177	40	132.139
1853801	22036740740790156497 663188023396082673867361	14614502533976550541040010234092567410394417	44	143.390
1853801	272057955679353506441 663188023396082673867361	180425577876169516387090884382073733493172201	45	147.016
1853801	11122807 22036740740790156497 272057955679353506441	66684238194495869991892726291173949912212815839	47	155.546
1853801	11122807 22036740740790156497 663188023396082673867361	16255429108643211419373361311183644744030689416851 9	51	166.797
1853801	11122807 272057955679353506441 663188023396082673867361	20068388805801034300569491984411203974139902094882 07	52	170.423
1853801	22036740740790156497 272057955679353506441 663188023396082673867361	39759916826643918994973381067916817977768617444648 45259759939897	64	211.273
1853801	11122807 22036740740790156497 272057955679353506441 663188023396082673867361	44224188119881276870472288775589265842085062249365 792109174677805930879	71	234.680

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-07-07T17:23:00	alpertron	Manual testing	500000	15000000	12		22036740740790156497 272057955679353506441	40	132.139	0.101	0.201	0.203	5.076%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2015-07-07T17:23:00

alpertron

Manual testing

500000

15000000

22036740740790156497
272057955679353506441

132.139

0.101

0.201

0.203

5.076%

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.346 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:	20.346 GHz-days
Estimated T-Level:	24.732

Digits	B1	Complete	FacMiss
20	11000	9.056	0.012%
25	50000	0.821	44.018%
30	250000	0.051	95.050%
35	1000000	0.002	99.767%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.283
50000	5000000	663188023396082673867361	4	0.277
50000	6600000		221	17.24
50000	6700000		7	0.550

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-17T00:31:41	Gordon Spence	haswell	50000	5000000						3	0.208
2019-01-15T23:34:09	tottenhoff	2013pc	50000	5000000						3	0.208
2020-06-20T22:38:08	kracker	O0	50000	5000000						3	0.208
2020-07-18T04:05:10	-Anonymous-	aws	50000	5000000						3	0.208
2020-09-10T02:28:41	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.484
2020-11-21T00:21:10	nordi	sweet16	50000	5000000	663188023396082673867361	79.134	4	2	7511661306422966	4	0.277
2021-01-18T21:32:17	arachnotron	DellLaptop	50000	5000000						7	0.484
2021-04-19T11:17:51	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.484
2021-07-29T23:00:24	Ahmed Azhad	c5.4xlarge.azf2	50000	6700000						7	0.550
2021-08-06T10:58:15	TJAOI	Manual testing	50000	6600000						221	17.24

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T06:59:14

Oliver Kruse

GTX-1

11122807

22036740740790156497

272057955679353506441

BC5120D5BEF7AADC

2017-10-05T21:20:16

Oliver Kruse

Manual testing

11122807

22036740740790156497

272057955679353506441

BC5120D5BEF7AA__

2017-11-11T03:59:27

kkmrkkblmbrbk

c4.xlarge

11122807

22036740740790156497

272057955679353506441

BC5120D5BEF7AA__

2020-11-21T19:06:42

rbanov

ccg_lnx01

11122807

22036740740790156497

272057955679353506441

663188023396082673867361

8CD016E5D66415EF

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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