M252163 Mersenne number exponent details

is 2 ²⁵²¹⁶³ - 1

has 75909 decimal digits

takes 0.001 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	117.8362	73.1343%	30000000	10120247026890	4,486.3114	23.4282%	4,604.1475	79.4285%	6.2941%
PrimeNet	2⁴⁰	0.0000	55.0000%	2600	70000	0.0001	14.2231%	0.0001	61.4004%	6.4004%
GPU72	2⁴⁴	0.0000	59.0909%	4500	110000	0.0001	10.1737%	0.0001	63.2529%	4.1620%
Difference	+23	+117.8361	+14.0434%	+29995500	+10120246916890	+4,486.3113	+13.2545%	+4,604.1475	+16.1756%	+16.1756%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
252163	165535454644605177527	21	67.166	328231054208201 738977 × 444169513	2007-08-17	738977	444169513	123.51	0.2026	0.3677
252163	557863490716227236361553	24	78.884	1106156515262404152 2³ × 3 × 157 × 293565954156689	2017-08-25	157	293565954156689	372,661	130,131	243,049

exponent	prime factors	composite factor	digits	bits*
252163	165535454644605177527 557863490716227236361553	92346186565337155207240558074573461122419431	44	146.050

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07T00:00:00	ANONYMOUS	v4_computers	95000	3800000		-		-	-	0.002	-	-	2.195%
2001-06-17T00:00:00	ANONYMOUS	v4_computers	100000	10000000		-		-	-	0.005	-	-	2.715%
2002-06-02T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.002	-	-	1.555%
2002-08-10T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.003	-	-	2.236%
2003-03-07T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.007	-	-	3.046%
2003-11-08T00:00:00	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.014	-	-	3.972%
2021-06-04T03:07:23	ViliamF	3	50000000	7150000000		-	skipped known factor: 165535454644605177527	-	-	3.554	-	-	14.150%
2021-08-22T14:25:19	Oliver Kruse	Ollaptop	30000000	3000000000	24	-	skipped known factor: 165535454644605177527	-	-	1.561	-	-	12.576%
2022-04-21T20:51:35	Oliver Kruse	Threadripper-PC	30000000	10120247026890		-	skipped known factor: 165535454644605177527	-	-	4,486	-	-	23.428%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-11-24T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.002	-	-
2000-04-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.010	-	-
2000-12-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.019	-	-
2001-02-18T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.038	-	-
2002-03-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.076	-	-
2004-02-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.152	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.900 GHz-days
Estimated T-Level:	27.648

Digits	B1	Curves	Complete	FacMiss
20	11000	620 / 100	6.200	0.197%
25	50000	620 / 280	2.214	10.880%
30	250000	339 / 640	0.530	58.855%

New Calculation Method

Total ECM effort:	15.900 GHz-days
Estimated T-Level:	27.648

Digits	B1	Complete	FacMiss
20	11000	45.226	0.000%
25	50000	6.393	0.167%
30	250000	0.669	51.218%
35	1000000	0.055	94.657%
40	3000000	0.004	99.632%

ECM Summary

B1	B2	factor	curves	GHz-days
		165535454644605177527	1	0.00000e+0
50000	5000000		281	1.680
250000	25000000		211	6.309
250000	25000000	557863490716227236361553	7	0.209
250000	37626580		14	0.489
250000	38500000		7	0.247
250000	125000000		100	6.965

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-08T16:41:00	George Woltman	D_P4Debug	50000	5000000						1	0.006
2007-08-17T08:08:00	Team_Bundu	bundu1			165535454644605177527	67.166		1		1	-
2014-08-22T10:14:00	TJAOI	Manual testing	50000	5000000						49	0.293
2015-01-09T16:37:00	TJAOI	Manual testing	50000	5000000						50	0.299
2015-09-11T20:14:00	TJAOI	Manual testing	50000	5000000						90	0.538
2016-03-04T13:11:42	TJAOI	Manual testing	50000	5000000						91	0.544
2017-08-25T10:14:59	TJAOI	Manual testing	250000	25000000						37	1.106
2017-08-25T10:14:59	TJAOI	Manual testing	250000	25000000	557863490716227236361553	78.884	7	2		7	0.209
2019-12-30T05:04:23	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-01T04:08:17	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-03T08:17:08	kracker	O0	250000	25000000						3	0.090
2020-01-05T07:37:28	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-07T11:34:16	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-09T16:40:29	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-11T21:36:08	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-14T02:59:32	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-16T07:19:19	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-18T13:35:40	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-20T22:52:09	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-23T06:22:14	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-25T14:59:16	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-28T03:34:07	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-30T18:47:22	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-02T21:00:25	MarkS	laptop64	250000	25000000						3	0.090
2020-02-05T20:20:32	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-09T02:45:10	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-12T22:37:14	MarkS	desktop-i7	250000	25000000						3	0.090
2020-02-16T10:04:10	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-19T12:49:53	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-23T03:04:24	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-24T10:20:12	TJAOI	Manual testing	250000	25000000						73	2.183
2021-01-19T02:14:30	seatsea	dt	250000	37626580						7	0.244
2021-02-14T16:13:09	mnd9	consult	250000	25000000						7	0.209
2021-04-12T05:51:17	Chang Chia-Tche	exbpc13	250000	25000000						7	0.209
2021-05-22T12:49:59	Chang Chia-Tche	exbpc13	250000	25000000						7	0.209
2021-07-14T09:01:29	seatsea	Manual testing	250000	37626580						7	0.244
2021-07-15T12:24:38	Eric	miniPCWindows	250000	38500000						7	0.247
2021-09-26T23:00:48	MarkS	laptop64	250000	25000000						7	0.209
2021-11-06T14:07:23	mnd9	f4	250000	25000000						7	0.209
2022-01-17T09:23:19	Oliver Kruse	11700K	250000	125000000						100	6.965

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2001-09-30T00:00:00	ANONYMOUS	v4_computers	6D5C5E9008D06E__	0.001

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-22T07:23:21

Oliver Kruse

Doppelherz

165535454644605177527

557863490716227236361553

05503CBD41E9CDF3

2017-09-22T10:03:04

Oliver Kruse

Manual testing

165535454644605177527

557863490716227236361553

05503CBD41E9CDF3

2017-09-28T13:10:07

alpertron

Manual testing

165535454644605177527

557863490716227236361553

05503CBD41E9CD__

2017-12-07T04:49:37

ATH

xps

165535454644605177527

557863490716227236361553

05503CBD41E9CD__

2020-04-17T20:15:13

Oliver Kruse

AddPrpType5

165535454644605177527

557863490716227236361553

921771F936405C__

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 = 30000000, B2 = 10120247026890 (P-1 stage 2)

B1 = 50000000, B2 = 7150000000 (P-1 stage 2)

B1 = 30000000, B2 = 3000000000 (P-1 stage 2)

B1 = 50000000 (P-1 stage 1)

B1 = 30000000 (P-1 stage 1)

B1 = 262144, B2 = 26214400 (P-1 stage 2)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 100000, B2 = 10000000 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 95000, B2 = 3800000 (P-1 stage 2)

B1 = 262144 (P-1 stage 1)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵³

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-21T20:51:35+00:00

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