M101 293 Mersenne number exponent details

is 2 ¹⁰¹²⁹³ - 1

has 30493 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	293.3462	74.6269%	1000000000	6735532633830	1,185.5068	25.4994%	1,478.8530	81.0969%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1592%	0.0000	62.9706%
Difference	+23	+293.3462	+13.2632%	+999998800	+6735532615830	+1,185.5068	+21.3402%	+1,478.8530	+18.1263%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
101293	6398177999055617244705713	25	82.404	31582527909409422392 2³ × 172421 × 22896375665819	2008-05-23	172421	22896375665819	14,634,226	4,019.6	7,507.5

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	-	-	4.292%
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	-	-	2.664%
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%
2021-12-19	Seth_Tr	Manual testing	1000000000	6735532633830		-		-	-	1,186	-	-	25.499%

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		-	-	0.190	-	-
2018-10-25	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.184	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷		-	-	0.190	-	-
2018-11-02	J.R. Allen	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2018-11-02	J.R. Allen	Manual testing	2⁵⁸	2⁵⁹		-	-	0.379	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.379	-	-
2018-11-02	J.R. Allen	Manual testing	2⁵⁹	2⁶⁰		-	-	0.758	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.758	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.516	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.033	-	-

ECM factoring results:

Total ECM effort:	12.563 GHz-days
Estimated T-Level:	30.756

Digits	B1	Complete	FacMiss
20	11000	81.913	0.000%
25	50000	12.886	0.000%
30	250000	1.542	21.402%
35	1000000	0.151	85.976%
40	3000000	0.013	98.746%

ECM Summary

B1	B2	factor	curves	GHz-days
		6398177999055617244705713	1	0.00000e+0
50000	5000000		266	0.618
250000	25000000		585	6.791
1000000	100000000		111	5.154

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-10	Steve Scott	Asus-1	50000	5000000						3	0.007
2008-01-10	Steve Scott	Gigabyte-1	50000	5000000						3	0.007
2008-01-11	Team_Bundu	bundu2	50000	5000000						3	0.007
2008-01-15	Team_Bundu	bundu1	50000	5000000						3	0.007
2008-01-22	Steve Scott	Abit-3	50000	5000000						3	0.007
2008-01-30	Team_Bundu	bundu4	50000	5000000						3	0.007
2008-02-05	Steve Scott	Abit-2	50000	5000000						3	0.007
2008-03-11	Scott Kurowski	UW4	50000	5000000						3	0.007
2008-05-18	Sturle Sunde	v17	50000	5000000						3	0.007
2008-05-23	George Woltman	Manual testing			6398177999055617244705713	82.404		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	50000	5000000						1	0.002
2010-01-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-16	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-16	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-16	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-16	Rob_Dee	twopc	50000	5000000						1	0.002
2010-04-20	James Hintz	NEW_OMFG	50000	5000000						11	0.026
2014-05-13	TJAOI	Manual testing	50000	5000000						220	0.511
2017-02-28	kkmrkkblmbrbk	kel1	250000	25000000						585	6.791
2019-01-26	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-01	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-07	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-13	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-20	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-26	Niels_Mache_Nextcloud	SuperDry-X	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
2019-03-21	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-28	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-03	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-18	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-04	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-12	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-31	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-23	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-18	Niels_Mache_Nextcloud		1000000	100000000						3	0.139
2019-07-27	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-18	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-02	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-09	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-17	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-02	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-09	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-17	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-31	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-11-08	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Charles F. Kerchner III		31FE4C0CD9E69A08	0.000

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

6398177999055617244705713

486B9255FFC648__

2017-09-21

Oliver Kruse

Manual testing

6398177999055617244705713

486B9255FFC648__

2017-09-22

Oliver Kruse

Manual testing

6398177999055617244705713

486B9255FFC648__

2017-11-06

kkmrkkblmbrbk

c4.xlarge

6398177999055617244705713

486B9255FFC648__

2020-04-17

Oliver Kruse

AddPrpType5

6398177999055617244705713

C82982F4D56418__

2022-04-15

LordJulius

WhiteBox

6398177999055617244705713

C82982F4D56418E6

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 = 6735532633830 (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)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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=30.76 ~= 86-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

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