M101 377 Mersenne number exponent details

is 2 ¹⁰¹³⁷⁷ - 1

has 30518 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	293.1031	74.6269%	1000000000	6738787135080	1,186.0782	25.5011%	1,479.1813	81.0973%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1600%	0.0000	62.9709%
Difference	+23	+293.1031	+13.2632%	+999998800	+6738787117080	+1,186.0782	+21.3412%	+1,479.1813	+18.1264%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
101377	4297937593748598158613817	25	81.830	21197794340671938204 2² × 3 × 23 × 587 × 971 × 134748599827	2017-03-03	971	134748599827	6,424,354	23.656	44.183
101377	16361265579902577382575697	26	83.758	80695155606807152424 2³ × 3 × 13² × 243473 × 81714421423	2009-10-04	243473	81714421423	33,225,963	14.346	26.793

exponent	prime factors	composite factor	digits	bits*
101377	4297937593748598158613817 16361265579902577382575697	70319698417168245895870325506985009411006592605449	50	165.588

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-11-25	ANONYMOUS	v4_computers	1000000	25000000		-		-	-	0.007	-	-	4.293%
2002-06-02	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.001	-	-	1.317%
2002-07-20	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.001	-	-	1.927%
2003-02-02	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.003	-	-	2.665%
2003-09-21	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.005	-	-	3.519%
2016-11-02	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-		-	-	0.656	-	-	11.735%
2021-12-18	Seth_Tr	Manual testing	1000000000	6738787135080		-	skipped known factor: 4297937593748598158613817 skipped known factor: 16361265579902577382575697	-	-	1,186	-	-	25.501%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-09-14	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.006	-	-
1999-12-30	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.012	-	-
2000-12-07	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.095	-	-
2000-12-14	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.095	-	-
2002-04-20	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.189	-	-
2018-10-25	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.183	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷		-	-	0.189	-	-
2022-03-07	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.189	-	-
2009-01-06	Sturle Sunde	ginglo.ifi	2⁵⁸	2⁵⁹		-	-	0.379	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.379	-	-
2009-02-03	monst	kingslake	2⁵⁹	2⁶⁰		-	-	0.758	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.758	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.515	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.030	-	-

ECM factoring results:

Total ECM effort:	12.623 GHz-days
Estimated T-Level:	30.754

Digits	B1	Complete	FacMiss
20	11000	83.521	0.000%
25	50000	13.001	0.000%
30	250000	1.545	21.333%
35	1000000	0.151	85.994%
40	3000000	0.013	98.749%

ECM Summary

B1	B2	factor	curves	GHz-days
		16361265579902577382575697	1	0.00000e+0
50000	5000000		322	0.748
250000	25000000		511	5.932
250000	25000000	4297937593748598158613817	68	0.789
1000000	100000000		111	5.154

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2003-11-28	eteo	v4_computers	50000	5000000						300	0.697
2009-07-21	Sturle Sunde	v17	250000	25000000						3	0.035
2009-08-10	Sturle Sunde	v17	250000	25000000						3	0.035
2009-08-20	Ryan Schulz	T7400	250000	25000000						3	0.035
2009-09-01	Sturle Sunde	v21	250000	25000000						3	0.035
2009-09-02	Ryan Schulz		250000	25000000						3	0.035
2009-09-13	Sturle Sunde	v22	250000	25000000						3	0.035
2009-09-21	Sturle Sunde	v22	250000	25000000						3	0.035
2009-09-27	Sturle Sunde	v22	250000	25000000						3	0.035
2009-10-04	James Hintz	ron3			16361265579902577382575697	83.758		1		1	-
2010-01-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-15	Rob_Dee	twopc	250000	25000000						1	0.012
2010-01-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-16	Rob_Dee	twopc	50000	5000000						4	0.009
2010-01-16	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-16	Rob_Dee	twopc	250000	25000000						1	0.012
2010-01-16	Rob_Dee	twopc	250000	25000000						1	0.012
2010-01-16	Rob_Dee	twopc	250000	25000000						1	0.012
2010-01-16	Rob_Dee	twopc	250000	25000000						1	0.012
2010-01-16	Rob_Dee	twopc	250000	25000000						1	0.012
2010-04-20	James Hintz	NEW_OMFG	50000	5000000						11	0.026
2010-05-22	Rob_Dee	twopc	50000	5000000						1	0.002
2010-05-22	Rob_Dee	twopc	50000	5000000						1	0.002
2010-05-23	Rob_Dee	twopc	50000	5000000						1	0.002
2017-03-03	kkmrkkblmbrbk	kel1	250000	25000000	4297937593748598158613817	81.830	68	2		68	0.789
2017-03-03	kkmrkkblmbrbk	kel1	250000	25000000						481	5.584
2019-01-27	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-02	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-20	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-04	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-09	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-22	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-29	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-04	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-10	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-27	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-05	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-13	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-21	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-01	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-12	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-20	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-07-28	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-12	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-19	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-03	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-10	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-17	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-25	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-02	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-10	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-17	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-25	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-01	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Robert Clark		10DB7CCDC99CA3D7	0.000

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

79A31F1714B8A1__

2017-09-21

Oliver Kruse

Manual testing

79A31F1714B8A1__

2017-10-09

Chang Chia-Tche

homura

79A31F1714B8A1__

2017-10-13

kkmrkkblmbrbk

Manual testing

4297937593748598158613817

16361265579902577382575697

79A31F1714B8A1__

2020-04-17

Oliver Kruse

AddPrpType5

4297937593748598158613817

16361265579902577382575697

A092979C7FF254__

2022-04-15

LordJulius

WhiteBox

4297937593748598158613817

16361265579902577382575697

A092979C7FF254EE

2022-10-27

LordJulius

WhiteBox

4297937593748598158613817

16361265579902577382575697

A092979C7FF254EE

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 = 6738787135080 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

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

B1 = 100000000 (P-1 stage 1)

B1 = 1000000, B2 = 25000000 (P-1 stage 2)

B1 = 262144, B2 = 26214400 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 262144 (P-1 stage 1)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁴

2⁵³

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=30.75 ~= 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