M29881 Mersenne number exponent details

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M29881

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is 2 ²⁹⁸⁸¹ - 1

has 8996 decimal digits

takes 0.000 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	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	994.4084	77.6119%	500000000	10000000000	0.8128	13.6945%	995.2212	80.6779%	3.0659%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.0993%	0.0000	64.0373%	1.5373%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7565%	0.0001	66.5079%	0.5988%
Difference	+23	+994.4083	+11.7028%	+499999500	+9999990000	+0.8128	+11.9380%	+995.2211	+14.1700%	+14.1700%

Known prime factors (4 factors, 266.1 bits, 0.89057780% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
29881	179287	6	17.452	3 3	-	1	3	5.847e-13	8.857e-10	1.626e-9
29881	651457504170017	15	49.211	10900865168 2⁴ × 127 × 1259 × 4261	2008-08-26	1259	4261	0.0041	1.136e-6	2.047e-6
29881	83357134187028156701162207	26	86.108	1394818349235771170663 1394818349235771170663	2009-05-10	1	1394818349235771170663	894,878,736	6.070e+10	1.134e+11
29881	13176000677894290663100195118072871	35	113.343	220474560387776357268836302635 3² × 5 × 29 × 127 × 2206778471 × 602817031886171	2017-10-03	2206778471	602817031886171	4.415e+12	26,234	48,994

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
29881	179287 651457504170017	116797861550129837879	21	66.663
29881	179287 83357134187028156701162207	14944850516989717130481268606409	32	103.559
29881	179287 13176000677894290663100195118072871	2362285633537633690115244682133930822977	40	130.795
29881	651457504170017 83357134187028156701162207	54303630592246562025335971389212822947519	41	135.318
29881	179287 651457504170017 83357134187028156701162207	9735935017992109365836410302457799387791838953	46	152.770
29881	651457504170017 13176000677894290663100195118072871	8583604516563466678487311629201043705163379308807	49	162.554
29881	179287 651457504170017 13176000677894290663100195118072871	15389287029611142503859546400645675227676267861380 80609	55	180.006
29881	83357134187028156701162207 13176000677894290663100195118072871	10983136565556083441188246802768498199239116078744 75817186297	61	199.451
29881	179287 83357134187028156701162207 13176000677894290663100195118072871	19691336054288535319203172045279557366469834044099 1145835879630239	66	216.903
29881	651457504170017 83357134187028156701162207 13176000677894290663100195118072871	71550467349556184200783746946880482833711010181653 6441008540101633250657049	75	248.662
29881	179287 651457504170017 83357134187028156701162207 13176000677894290663100195118072871	12828068639699879596805915638865361125807545882438 1368899098129201520610550344063	81	266.114

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2017-01-04T01:58:23	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-	skipped known factor: 179287 skipped known factor: 651457504170017	-	-	0.813	-	-	13.695%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-10-25T00:00:00	GrunwalderGIMP	v4_computers	?	?	651457504170017	49.211	15	0.002	3.37317e-5	0.003
2008-08-26T19:59:00	ANONYMOUS	Manual testing	?	?	651457504170017	49.211	15	0.002	3.37317e-5	0.003

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.119 GHz-days
Estimated T-Level:	31.617

Digits	B1	Curves	Complete	FacMiss
20	11000	1221 / 100	12.210	0.000%
25	50000	1221 / 280	4.361	1.267%
30	250000	1096 / 640	1.713	18.017%
35	1000000	511 / 1580	0.323	72.360%
40	3000000	500 / 4700	0.106	89.907%

New Calculation Method

Total ECM effort:	19.119 GHz-days
Estimated T-Level:	31.617

Digits	B1	Complete	FacMiss
20	11000	154.354	0.000%
25	50000	31.536	0.000%
30	250000	5.462	0.425%
35	1000000	0.794	45.208%
40	3000000	0.098	90.639%
45	11000000	0.011	98.945%
50	44000000	0.001	99.899%

ECM Summary

B1	B2	factor	curves	GHz-days
		83357134187028156701162207	1	0.00000e+0
50000	5000000		125	0.072
250000	25000000		585	1.681
1000000	100000000		11	0.126
3000000	300000000		110	3.793
3000000	300000000	13176000677894290663100195118072871	390	13.45

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-04T14:32:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.017
2009-05-10T17:34:00	Matthias Wurtinger	WUR_E6600	250000	25000000						0	-
2009-05-10T17:34:00	Matthias Wurtinger	WUR_E6600			83357134187028156701162207	86.108		1		1	-
2009-10-15T21:34:00	GrunwalderGIMP	GWPrime02	50000	5000000						95	0.055
2011-01-19T04:29:00	James Hintz	NEW_OMFG	250000	25000000						11	0.032
2011-03-18T19:12:00	James Hintz	17_051310	250000	25000000						11	0.032
2014-12-05T22:51:00	James Hintz	08_04_2014	250000	25000000						563	1.618
2014-12-05T23:19:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2017-10-03T11:06:08	nordi	nordiputer	3000000	300000000	13176000677894290663100195118072871	113.343	390	2		390	13.45
2017-10-06T19:23:53	nordi	nordiputer	3000000	300000000						110	3.793

Lucas-Lehmer results:
No L-L results for M29881

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:40:05

Oliver Kruse

Ollaptop

5F0DA2AD66B4A0__

2017-09-21T20:27:21

Oliver Kruse

Manual testing

5F0DA2AD66B4A0__

2017-10-02T10:30:00

kkmrkkblmbrbk

Manual testing

179287

651457504170017

83357134187028156701162207

5F0DA2AD66B4A0__

2017-10-03T15:07:51

Oliver Kruse

GTX-1

179287

651457504170017

83357134187028156701162207

13176000677894290663100195118072871

C8B4B4C734BF2225

2017-10-04T13:31:32

kkmrkkblmbrbk

Manual testing

179287

651457504170017

83357134187028156701162207

13176000677894290663100195118072871

C8B4B4C734BF22__

2017-10-09T01:00:46

Chang Chia-Tche

homura

C8B4B4C734BF22__

2017-10-13T18:19:51

Oliver Kruse

Threadripper

C8B4B4C734BF22__

2020-04-17T13:47:21

Oliver Kruse

Manual testing

179287

651457504170017

83357134187028156701162207

13176000677894290663100195118072871

2C300F104D082E__

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 = 500000000, B2 = 10000000000 (P-1 stage 2)

B1 = 500000000 (P-1 stage 1)

10⁰

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10⁴

10⁵

10⁶

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10⁹

10¹⁰

10⁰

10¹

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10³

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10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

TF factor-bounds graph:

2⁶⁷

2¹⁰

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

Last modified: 2020-04-17T13:47:21+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