M101 027 Mersenne number exponent details

is 2 ¹⁰¹⁰²⁷ - 1

has 30413 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	294.1186	74.6269%	1000000000	6548112641070	1,152.6042	25.4544%	1,446.7228	81.0854%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1568%	0.0000	62.9697%
Difference	+23	+294.1186	+13.2632%	+999998800	+6548112623070	+1,152.6042	+21.2976%	+1,446.7228	+18.1158%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
101027	969253039	9	29.852	4797 3² × 13 × 41	-	13	41	7.351e-10	4.680e-8	8.525e-8
101027	716140752533361425229261778303	30	99.176	3544303763020585710895413 3 × 383 × 499 × 44988589 × 137406725167	2021-12-17	44988589	137406725167	1.754e+12	24.260	45.054

exponent	prime factors	composite factor	digits	bits*
101027	969253039 716140752533361425229261778303	694121600744707510288833250346727012817	39	129.028

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-11-02	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-	skipped known factor: 969253039	-	-	0.656	-	-	11.732%
2021-12-17	Seth_Tr	Manual testing	1000000000	6548112641070			716140752533361425229261778303	30	99.176	1,153	0.000	2,305	25.454%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2018-10-21	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.184	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	969253039	29.852	9	7.35062e-10	0.000	1.56839e-9
2018-10-21	J.R. Allen	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2018-10-21	J.R. Allen	Manual testing	2⁵⁸	2⁵⁹		-	-	0.380	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.380	-	-
2018-10-21	J.R. Allen	Manual testing	2⁵⁹	2⁶⁰		-	-	0.760	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.760	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.520	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.041	-	-
2022-11-07	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.72	-	-
2022-11-07	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.43	-	-
2022-11-07	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	36.98	-	-
2022-11-07	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	73.97	-	-
2022-11-07	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	147.9	-	-

ECM factoring results:

Total ECM effort:	12.597 GHz-days
Estimated T-Level:	30.756

Digits	B1	Complete	FacMiss
20	11000	82.490	0.000%
25	50000	12.939	0.000%
30	250000	1.545	21.330%
35	1000000	0.151	85.963%
40	3000000	0.013	98.746%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	281	0.652
250000	25000000	585	6.791
1000000	100000000	111	5.154

	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
2010-04-20	James Hintz	NEW_OMFG	50000	5000000						11	0.026
2014-04-11	TJAOI	Manual testing	50000	5000000						38	0.088
2014-05-13	TJAOI	Manual testing	50000	5000000						231	0.536
2017-02-14	kkmrkkblmbrbk	kel1	250000	25000000						585	6.791
2019-01-26	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-01-31	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-06	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-12	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-03	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-08	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-13	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-20	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-27	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-02	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-03	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-11	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-29	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-08	Niels_Mache_Nextcloud		1000000	100000000						3	0.139
2019-07-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-02	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-08-09	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-17	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-31	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-15	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-30	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-07	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-15	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-22	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-30	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-06	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M101027

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Ollaptop

969253039

EA442566DBF203__

2017-09-21

Oliver Kruse

Manual testing

969253039

EA442566DBF203__

2017-10-13

kkmrkkblmbrbk

Manual testing

969253039

EA442566DBF203__

2020-04-17

Oliver Kruse

AddPrpType5

969253039

508B174D3FE0D8__

2021-12-17

SRJ2877

LTOS

969253039

716140752533361425229261778303

508B174D3FE0D833

2022-04-15

LordJulius

WhiteBox

969253039

716140752533361425229261778303

508B174D3FE0D833

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 = 6548112641070 (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: 67.8

ECM T-Level=30.76 ~= 86-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2023-04-26T21:34:10+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