M100 523 Mersenne number exponent details

is 2 ¹⁰⁰⁵²³ - 1

has 30261 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	295.5932	74.6269%	1000000000	6552834288000	1,153.4331	25.4495%	1,449.0264	81.0842%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1521%	0.0000	62.9679%
Difference	+23	+295.5932	+13.2632%	+999998800	+6552834270000	+1,153.4331	+21.2974%	+1,449.0263	+18.1163%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100523	1229001636703	13	40.161	6113037 3 × 7 × 97 × 3001	-	97	3001	1.702e-6	8.224e-7	9.838e-7
100523	265722819270463	15	47.917	1321701597 3³ × 48951911	2010-01-20	27	48951911	0.0003	0.0086	0.0161

exponent	prime factors	composite factor	digits	bits*
100523	1229001636703 265722819270463	326573779792734495424603489	27	88.078

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: 1229001636703 skipped known factor: 265722819270463	-	-	0.656	-	-	11.728%
2021-12-17	Seth_Tr	Manual testing	1000000000	6552834288000		-	skipped known factor: 1229001636703 skipped known factor: 265722819270463	-	-	1,153	-	-	25.449%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2018-10-25	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.185	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	1229001636703	40.161	13	1.70219e-6	0.000	3.61177e-6
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	265722819270463	47.917	15	0.000	0.000	0.001
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		-	-	0.382	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.382	-	-
2018-11-01	J.R. Allen	Manual testing	2⁵⁹	2⁶⁰		-	-	0.764	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.764	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.528	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.056	-	-
2022-10-22	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.77	-	-
2022-10-22	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.53	-	-
2022-10-22	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	37.17	-	-
2022-10-23	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	74.34	-	-
2022-10-23	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	148.7	-	-

ECM factoring results:

Total ECM effort:	12.733 GHz-days
Estimated T-Level:	30.766

Digits	B1	Complete	FacMiss
20	11000	82.951	0.000%
25	50000	13.036	0.000%
30	250000	1.560	21.008%
35	1000000	0.153	85.798%
40	3000000	0.013	98.726%

ECM Summary

B1	B2	factor	curves	GHz-days
		265722819270463	1	0.00000e+0
50000	5000000		280	0.650
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
2010-01-20	Rob_Dee	twopc			265722819270463	47.917		1		1	-
2010-01-20	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-21	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-21	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-22	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-22	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-22	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-22	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-22	Rob_Dee	twopc	50000	5000000						1	0.002
2014-04-11	TJAOI	Manual testing	50000	5000000						40	0.093
2014-05-19	TJAOI	Manual testing	50000	5000000						231	0.536
2017-01-24	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	SuperDry3	1000000	100000000						3	0.139
2019-02-05	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-11	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-17	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-23	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-01	Niels_Mache_Nextcloud	SuperDry-X	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
2019-03-18	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-31	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-06	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-13	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-23	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-29	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-08	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-05	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-07-30	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-06	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-08-13	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-21	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-08-28	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-04	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-12	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-19	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-27	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-19	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-02	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-09	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M100523

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

1229001636703

265722819270463

7983BCBDF18A75__

2017-09-21

Oliver Kruse

Manual testing

1229001636703

265722819270463

7983BCBDF18A75__

2017-10-13

kkmrkkblmbrbk

Manual testing

1229001636703

265722819270463

7983BCBDF18A75__

2020-04-17

Oliver Kruse

AddPrpType5

1229001636703

265722819270463

454F801F08D360__

2022-04-15

LordJulius

WhiteBox

1229001636703

265722819270463

454F801F08D360B8

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 = 6552834288000 (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

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=30.77 ~= 86-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

Last modified: 2023-03-23T17:39:31+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