M100 649 Mersenne number exponent details

is 2 ¹⁰⁰⁶⁴⁹ - 1

has 30299 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	295.2232	74.6269%	1000000000	40982915833860	7,197.8252	28.1109%	7,493.0484	81.7595%
Target	2⁴⁴	0.0000	61.3636%	1200	144000	0.0000	4.1533%	0.0001	62.9683%
Difference	+23	+295.2232	+13.2632%	+999998800	+40982915689860	+7,197.8252	+23.9576%	+7,493.0483	+18.7912%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100649	238558058503	12	37.796	1185099 3 × 31 × 12743	-	31	12743	2.756e-7	2.332e-6	4.178e-6
100649	5199160008792727	16	52.207	25828175187 3³ × 73 × 13104097	2008-08-26	73	13104097	0.0066	0.0023	0.0043

exponent	prime factors	composite factor	digits	bits*
100649	238558058503 5199160008792727	1240301517544033362066907681	28	90.003

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-10-31	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-	skipped known factor: 238558058503 skipped known factor: 5199160008792727	-	-	0.656	-	-	11.729%
2021-12-16	Seth_Tr	Manual testing	1000000000	40982915833860		-	skipped known factor: 238558058503 skipped known factor: 5199160008792727	-	-	7,198	-	-	28.111%

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	?	?	5199160008792727	52.207	16	0.001	0.000	0.001
2018-11-01	J.R. Allen	Manual testing	2⁵³	2⁵⁷		-	-	0.179	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	238558058503	37.796	12	2.75587e-7	0.000	5.87813e-7
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	5199160008792727	52.207	16	0.007	0.000	0.013
2018-11-01	J.R. Allen	Manual testing	2⁵⁷	2⁵⁸		-	-	0.191	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.191	-	-
2018-11-01	J.R. Allen	Manual testing	2⁵⁸	2⁵⁹		-	-	0.381	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.381	-	-
2018-11-01	J.R. Allen	Manual testing	2⁵⁹	2⁶⁰		-	-	0.763	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.763	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.526	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.052	-	-
2022-10-23	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.75	-	-
2022-10-23	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.51	-	-
2022-10-23	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	37.12	-	-
2022-10-23	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	74.25	-	-
2022-10-24	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	148.5	-	-

ECM factoring results:

Total ECM effort:	12.736 GHz-days
Estimated T-Level:	30.766

Digits	B1	Complete	FacMiss
20	11000	82.990	0.000%
25	50000	13.039	0.000%
30	250000	1.561	21.003%
35	1000000	0.153	85.797%
40	3000000	0.013	98.726%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	281	0.652
250000	25000000	585	6.790
1000000	100000000	114	5.293

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-01-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-04-19	James Hintz	NEW_OMFG	50000	5000000						11	0.026
2014-04-11	TJAOI	Manual testing	50000	5000000						38	0.088
2014-06-09	TJAOI	Manual testing	50000	5000000						231	0.536
2017-01-29	kkmrkkblmbrbk	kel1	250000	25000000						585	6.790
2019-01-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-01-30	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-05	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-17	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-23	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-01	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-07	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-11	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-25	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-01	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-07	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-13	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-24	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-30	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-15	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-06	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-17	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-28	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-07-31	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-07	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-14	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-08-22	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-08-29	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-05	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-13	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-20	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-27	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-05	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-12	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-20	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-27	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-03	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-10	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M100649

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

238558058503

5199160008792727

D69E7EDD947299__

2017-09-21

Oliver Kruse

Manual testing

238558058503

5199160008792727

D69E7EDD947299__

2017-10-13

kkmrkkblmbrbk

Manual testing

238558058503

5199160008792727

D69E7EDD947299__

2020-04-17

Oliver Kruse

AddPrpType5

238558058503

5199160008792727

A074B763A0899C__

2022-04-15

LordJulius

WhiteBox

238558058503

5199160008792727

A074B763A0899C63

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 = 40982915833860 (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:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

this exponent TF target: 44

TF double-checked to: 67.8

ECM T-Level=30.77 ~= 86-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

Last modified: 2023-06-05T21:50:05+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