M100 501 Mersenne number exponent details

is 2 ¹⁰⁰⁵⁰¹ - 1

has 30254 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	295.6579	74.6269%	1000000000	12345532399200	2,170.3735	26.3824%	2,466.0314	81.3209%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1519%	0.0000	62.9678%
Difference	+23	+295.6579	+13.2632%	+999998800	+12345532381200	+2,170.3735	+22.2305%	+2,466.0314	+18.3531%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100501	33768337	8	25.009	168 2³ × 3 × 7	-	8	8	4.610e-11	2.578e-8	5.246e-8
100501	491674545022107113	18	58.770	2446117675556 2² × 29 × 887 × 23773643	2010-01-28	887	23773643	0.5107	0.0042	0.0078
100501	15451045243326914782921	23	73.710	76870106980661460 2² × 3 × 5 × 19 × 29 × 1109 × 2096636249	2010-01-31	1109	2096636249	27,932	0.3681	0.6875
100501	8225833261839371881359579980833	31	102.698	40924136385903482957182416 2⁴ × 3 × 271 × 3146074445410784360177	2017-01-20	271	3146074445410784360177	1.780e+12	5.523e+11	1.032e+12

exponent	prime factors	composite factor	digits	bits*
100501	33768337 491674545022107113	16603031730628185441881081	26	83.780
100501	33768337 15451045243326914782921	521756102778910259559958172377	30	98.719
100501	33768337 8225833261839371881359579980833	277772709691601149558074314971222284721	39	127.707
100501	491674545022107113 15451045243326914782921	7596885640128753115308797046992405017073	40	132.481
100501	33768337 491674545022107113 15451045243326914782921	256534194446328458587547317747444369057011817601	48	157.490
100501	491674545022107113 8225833261839371881359579980833	4044432826442588458291907050497412824253812965129	49	161.468
100501	15451045243326914782921 8225833261839371881359579980833	12709772189274354683272745824709341428319675753575 3193	54	176.408
100501	33768337 491674545022107113 8225833261839371881359579980833	13657377065717583821191156165387265387752452974144 5320473	57	186.478
100501	33768337 15451045243326914782921 8225833261839371881359579980833	42918787048064419440228234392412796839956015457746 03370050041	61	201.417
100501	491674545022107113 15451045243326914782921 8225833261839371881359579980833	62490714584960985890592919612498050057858542937981 217120648682377761809	71	235.179
100501	33768337 491674545022107113 15451045243326914782921 8225833261839371881359579980833	21102075094757777034057868392887435661966367762587 19839400234365138222072041633	79	260.188

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: 33768337 skipped known factor: 491674545022107113	-	-	0.656	-	-	11.728%
2021-12-16	Seth_Tr	Manual testing	1000000000	12345532399200		-	skipped known factor: 33768337 skipped known factor: 491674545022107113 skipped known factor: 15451045243326914782921	-	-	2,170	-	-	26.382%

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	33768337	25.009	8	4.60952e-11	0.000	9.84100e-11
2018-11-01	J.R. Allen	Manual testing	2⁵⁷	2⁵⁸		-	-	0.191	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.191	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹	491674545022107113	58.770	18	0.129	0.000	0.261
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		-	-	19.54	-	-
2022-10-22	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	37.18	-	-
2022-10-22	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	74.35	-	-
2022-10-22	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	148.7	-	-

ECM factoring results:

Total ECM effort:	12.731 GHz-days
Estimated T-Level:	30.766

Digits	B1	Complete	FacMiss
20	11000	82.913	0.000%
25	50000	13.032	0.000%
30	250000	1.560	21.012%
35	1000000	0.153	85.799%
40	3000000	0.013	98.726%

ECM Summary

B1	B2	factor	curves	GHz-days
		491674545022107113	1	0.00000e+0
		15451045243326914782921	1	0.00000e+0
50000	5000000		279	0.648
250000	25000000		540	6.268
250000	25000000	8225833261839371881359579980833	45	0.522
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
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc			491674545022107113	58.770		1		1	-
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-30	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-30	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-30	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-30	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-30	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-31	Rob_Dee	twopc			15451045243326914782921	73.710		1		1	-
2010-01-31	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-31	Rob_Dee	twopc	50000	5000000						1	0.002
2014-04-11	TJAOI	Manual testing	50000	5000000						30	0.070
2014-05-19	TJAOI	Manual testing	50000	5000000						231	0.536
2017-01-21	kkmrkkblmbrbk	kel1	250000	25000000	8225833261839371881359579980833	102.698	45	2		45	0.522
2017-01-21	kkmrkkblmbrbk	kel1	250000	25000000						540	6.268
2019-01-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-01-30	Niels_Mache_Nextcloud	SuperDry-JP	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	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	SuperDry3	1000000	100000000						3	0.139
2019-03-11	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-31	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-06	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-12	Niels_Mache_Nextcloud	SuperDry3	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
2019-05-07	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-14	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-04	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	SuperDry3	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
2019-09-26	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	SuperDry3	1000000	100000000						3	0.139
2019-10-18	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 M100501

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Doppelherz

33768337

491674545022107113

15451045243326914782921

8225833261839371881359579980833

467DB3F985D0F3FB

2017-09-21

Oliver Kruse

Manual testing

33768337

491674545022107113

15451045243326914782921

8225833261839371881359579980833

467DB3F985D0F3FB

2017-09-22

Oliver Kruse

Manual testing

33768337

491674545022107113

15451045243326914782921

8225833261839371881359579980833

467DB3F985D0F3FB

2017-11-06

kkmrkkblmbrbk

c4.xlarge

33768337

491674545022107113

15451045243326914782921

8225833261839371881359579980833

467DB3F985D0F3__

2020-04-17

Oliver Kruse

AddPrpType5

33768337

491674545022107113

15451045243326914782921

8225833261839371881359579980833

0615D4F52DC2F6__

2022-04-15

LordJulius

WhiteBox

33768337

491674545022107113

15451045243326914782921

8225833261839371881359579980833

0615D4F52DC2F6CC

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 = 12345532399200 (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

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

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

2¹⁰⁰

2¹¹⁰

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