M72 977 Mersenne number exponent details

is 2 ⁷²⁹⁷⁷ - 1

has 21969 decimal digits

takes 0.000 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
Actual	2⁶⁷	407.1683	74.6269%	1000000000	95443272064140	11,039.7563	28.8912%	11,446.9245	81.9575%
Target	2⁴⁴	0.0000	61.3636%	500	10000	0.0000	2.2716%	0.0000	62.2413%
Difference	+23	+407.1682	+13.2632%	+999999500	+95443272054140	+11,039.7563	+26.6196%	+11,446.9245	+19.7162%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
72977	19265929	8	24.200	132 2² × 3 × 11	-	4	11	3.150e-11	9.300e-9	1.728e-8
72977	955122977	9	29.831	6544 2⁴ × 409	2008-08-26	16	409	1.388e-9	7.941e-8	8.744e-8
72977	3170042648657	13	41.528	21719464 2³ × 13 × 97 × 2153	2008-08-26	97	2153	4.748e-6	4.437e-7	4.657e-7
72977	548711313071030182176874106881	30	98.792	3759481158933843417630720 2¹¹ × 3 × 5 × 6007 × 92503 × 220238505631	2017-01-25	92503	220238505631	1.028e+12	25.470	47.571
72977	3060143196756072283354825720338808031833	40	131.169	20966490789948012958567944149107308 2² × 3 × 13 × 227 × 24499 × 4173989 × 79768109 × 72584909141	2017-01-25	79768109	72584909141	2.100e+12	8.5543	15.678

exponent	prime factors	composite factor	digits	bits*
72977	19265929 955122977	18401331461150633	17	54.031
72977	19265929 3170042648657	61073816595997707353	20	65.727
72977	955122977 3170042648657	3027780571802238891889	22	71.359
72977	19265929 955122977 3170042648657	58333005523921336532172149881	29	95.558
72977	19265929 548711313071030182176874106881	10571433199123239446676721985107757449	38	122.992
72977	955122977 548711313071030182176874106881	524086782853981360057628337518396904737	39	128.623
72977	3170042648657 548711313071030182176874106881	1739438264235748863483567227829886549108817	43	140.320
72977	19265929 955122977 548711313071030182176874106881	10097018748303222250193703459017470960482805673	47	152.823
72977	19265929 3060143196756072283354825720338808031833	58956501558535518929981954135421331485924317857	47	155.368
72977	955122977 3060143196756072283354825720338808031833	2922813080131956502105048689326171775995845726841	49	161.000
72977	19265929 3170042648657 548711313071030182176874106881	33511894098649176865705098878097418333185481595993	50	164.519
72977	955122977 3170042648657 548711313071030182176874106881	16613774532445610843147913212245184903570699899882 09	52	170.151
72977	3170042648657 3060143196756072283354825720338808031833	97007844447143184714742775402454629686581484906982 81	52	172.696
72977	19265929 955122977 3060143196756072283354825720338808031833	56310709282093584600644218590101083278139868068272 100289	56	185.199
72977	19265929 955122977 3170042648657 548711313071030182176874106881	32007980056410533486571783244527766294406495075143 545431161	59	194.350
72977	19265929 3170042648657 3060143196756072283354825720338808031833	18689462435617048495481195641666373212629711409325 0242168049	60	196.896
72977	955122977 3170042648657 3060143196756072283354825720338808031833	92654421180708317730006015431634839013680284817437 98957502537	61	202.528
72977	19265929 955122977 3170042648657 3060143196756072283354825720338808031833	17850735000036226190957370628787811623639943959925 3826905517895161873	69	226.727
72977	548711313071030182176874106881 3060143196756072283354825720338808031833	16791351916774042920754401846393255430278410245994 93930960571292342873	70	229.961
72977	19265929 548711313071030182176874106881 3060143196756072283354825720338808031833	32350099384258261995420693241008136519860830203221 103509817268317716034874017	77	254.160
72977	955122977 548711313071030182176874106881 3060143196756072283354825720338808031833	16037806030603880110796719377381422839288931132981 98876032493322363262164492921	79	259.792
72977	3170042648657 548711313071030182176874106881 3060143196756072283354825720338808031833	53229301704782180847494484385732206706620519811137 04433524046115812478587916971561	82	271.488
72977	19265929 955122977 548711313071030182176874106881 3060143196756072283354825720338808031833	30898323230138618133912172895755469834071895769392 055373521818041624721069506936988609	86	283.991
72977	19265929 3170042648657 548711313071030182176874106881 3060143196756072283354825720338808031833	10255119473639124566729885640671253074230747646244 5970543259492259968989788828631989245169	90	295.688
72977	955122977 3170042648657 548711313071030182176874106881 3060143196756072283354825720338808031833	50840529107902731707611314917580561594406756491300 69154045585527220101322640014106166657097	91	301.320
72977	19265929 955122977 3170042648657 548711313071030182176874106881 3060143196756072283354825720338808031833	97949002411528736798488835279874795145796736768168 824086932313530850039454788604328405277798148113	98	325.519

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-11-27	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-	skipped known factor: 19265929 skipped known factor: 955122977 skipped known factor: 3170042648657	-	-	0.432	-	-	11.454%
2017-01-25	kkmrkkblmbrbk	Manual testing	100000000	12720901946406			548711313071030182176874106881 3060143196756072283354825720338808031833	70	229.961	1,471	0.000	2,943	23.696%
2022-05-13	George Woltman	h110itx2	1000000000	1000000000		-	skipped known factor: 19265929 skipped known factor: 955122977 skipped known factor: 3170042648657	-	-	2.123	-	-	10.469%
2022-05-22	George Woltman	SkylakeX	1000000000	95443272064140		-	skipped known factor: 19265929 skipped known factor: 955122977 skipped known factor: 3170042648657 skipped known factor: 548711313071030182176874106881 skipped known factor: 3060143196756072283354825720338808031833	-	-	11,040	-	-	28.891%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26	ANONYMOUS	Manual testing	?	?	3170042648657	41.528	13	7.33344e-7	0.000	1.64685e-6
2008-08-26	ANONYMOUS	Manual testing	?	?	955122977	29.831	9	4.08141e-10	0.000	9.47219e-10

ECM factoring results:

Total ECM effort:	1,501.979 GHz-days
Estimated T-Level:	31.111

Digits	B1	Complete	FacMiss
20	11000	103.324	0.000%
25	50000	16.917	0.000%
30	250000	2.135	11.820%
35	1000000	0.222	80.070%
40	3000000	0.020	98.051%
45	11000000	0.002	99.850%

ECM Summary

B1	B2	factor	curves	GHz-days
11000	1100000		30	0.010
50000	5000000		274	0.418
250000	25000000		629	4.803
1000000	100000000		210	6.414
1000000	15000000000000	19265929 955122977 3170042648657	1	1,490

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-20	Matthias Wurtinger	WUR_E6600	11000	1100000						30	0.010
2010-04-26	James Hintz	06_122109	50000	5000000						11	0.017
2011-01-08	James Hintz	NEW_OMFG	50000	5000000						2	0.003
2011-01-19	James Hintz	OMFG	50000	5000000						11	0.017
2011-01-20	James Hintz	mom3	50000	5000000						10	0.015
2011-03-01	James Hintz	OMFG	50000	5000000						9	0.014
2011-04-30	James Hintz	NEW_OMFG	50000	5000000						50	0.076
2014-07-03	TJAOI	Manual testing	50000	5000000						181	0.276
2017-01-20	TJAOI	Manual testing	250000	25000000						44	0.336
2017-01-25	kkmrkkblmbrbk	x116xl	250000	25000000						585	4.467
2017-01-27	NoPolarBearsHere	Manual testing	1000000	15000000000000	19265929 955122977 3170042648657	95.558	1	2		1	1,490
2018-11-28	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.092
2018-12-02	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2018-12-05	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2018-12-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2018-12-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2018-12-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2018-12-17	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2018-12-21	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2018-12-23	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2018-12-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2018-12-30	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2019-01-03	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-01-07	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2019-01-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-01-14	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.092
2019-01-16	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.092
2019-01-22	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2019-01-26	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2019-01-30	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-02-03	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-02-07	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-02-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-02-16	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2019-02-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-02-24	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2019-02-28	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.092
2019-03-05	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-03-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2019-03-11	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2019-03-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-03-21	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.092
2019-03-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-03-30	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-04-04	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2019-04-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.092
2019-04-13	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-04-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-04-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-05-01	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-05-06	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2019-05-12	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.092
2019-05-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-05-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-06-01	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-06-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-06-17	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-06-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.092
2019-07-11	Niels_Mache_Nextcloud		1000000	100000000						3	0.092
2019-07-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-07-29	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-08-03	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.092
2019-08-09	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.092
2019-08-14	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.092
2019-08-19	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.092
2019-08-24	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.092
2019-08-29	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-09-03	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-09-08	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-09-14	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-09-19	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-09-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-09-29	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.092
2019-10-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-10-09	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-10-15	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-10-20	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-10-25	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-10-30	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-11-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092
2019-11-09	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.092

Lucas-Lehmer results:
No L-L results for M72977

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

19265929

955122977

3170042648657

548711313071030182176874106881

3060143196756072283354825720338808031833

B1AE07CAAB5E4114

2017-09-21

Oliver Kruse

Manual testing

19265929

955122977

3170042648657

548711313071030182176874106881

3060143196756072283354825720338808031833

B1AE07CAAB5E4114

2017-10-02

kkmrkkblmbrbk

Manual testing

19265929

955122977

3170042648657

548711313071030182176874106881

3060143196756072283354825720338808031833

B1AE07CAAB5E41__

2017-12-07

ATH

xps

19265929

955122977

3170042648657

548711313071030182176874106881

3060143196756072283354825720338808031833

B1AE07CAAB5E41__

2020-04-17

Oliver Kruse

AddPrpType5

19265929

955122977

3170042648657

548711313071030182176874106881

3060143196756072283354825720338808031833

719356CA3F03F7__

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 = 1000000000, B2 = 95443272064140 (P-1 stage 2)

B1 = 100000000, B2 = 12720901946406 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

B1 = 100000000, B2 = 2000000000 (P-1 stage 2)

B1 = 100000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=31.11 ~= 87-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

Last modified: 2023-03-25T13:08:14+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