M101 107 Mersenne number exponent details

is 2 ¹⁰¹¹⁰⁷ - 1

has 30437 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	293.8859	74.6269%	1000000000	6567654483390	1,156.0349	25.4597%	1,449.9208	81.0868%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1575%	0.0000	62.9699%
Difference	+23	+293.8858	+13.2632%	+999998800	+6567654465390	+1,156.0349	+21.3023%	+1,449.9207	+18.1169%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
101107	1011071	7	19.947	5 5	-	1	5	6.915e-13	3.924e-9	6.558e-9
101107	3437639	7	21.713	17 17	2008-07-26	1	17	2.773e-12	6.031e-9	6.558e-9
101107	13677629613203393	17	53.603	67639380128 2⁵ × 31 × 179 × 313 × 1217	2008-08-26	313	1217	0.0174	1.167e-6	2.053e-6
101107	2689135741713702483793673788961	31	101.085	13298464704291999979198640 2⁴ × 5 × 73 × 4967 × 243541957 × 1882438109	2019-08-17	243541957	1882438109	1.677e+12	1.0725	1.5971

exponent	prime factors	composite factor	digits	bits*
101107	1011071 3437639	3475697101369	13	41.660
101107	1011071 13677629613203393	13829054650651167763903	23	73.550
101107	3437639 13677629613203393	47018752985902898709127	23	75.316
101107	1011071 3437639 13677629613203393	47539297600209829700735745017	29	95.263
101107	1011071 2689135741713702483793673788961	2718907163510214883991753551478587231	37	121.032
101107	3437639 2689135741713702483793673788961	9244277902008950492686000970210103079	37	122.798
101107	1011071 3437639 2689135741713702483793673788961	9346621302662091583590527686951299130187609	43	142.745
101107	13677629613203393 2689135741713702483793673788961	36781002654787007846122380287241132795051144673	47	154.688
101107	1011071 13677629613203393 2689135741713702483793673788961	37188205135178154809986801159401179376225155895674 783	53	174.635
101107	3437639 13677629613203393 2689135741713702483793673788961	12643980918519935486513629324825132050044682192254 7047	54	176.401
101107	1011071 3437639 13677629613203393 2689135741713702483793673788961	12783962431268869692284821715080271086970726868805 1565357337	60	196.348

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: 1011071 skipped known factor: 3437639 skipped known factor: 13677629613203393	-	-	0.656	-	-	11.733%
2021-12-18	Seth_Tr	Manual testing	1000000000	6567654483390		-	skipped known factor: 1011071 skipped known factor: 3437639 skipped known factor: 13677629613203393 skipped known factor: 2689135741713702483793673788961	-	-	1,156	-	-	25.460%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-26	J Feitsma	Manual testing	?	?	3437639	21.713	7	1.01676e-14	0.000	2.16926e-14
2008-08-26	ANONYMOUS	Manual testing	?	?	13677629613203393	53.603	17	0.006	0.000	0.011
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	1011071	19.947	7	6.91545e-13	0.000	1.47541e-12
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	13677629613203393	53.603	17	0.017	0.000	0.035
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	3437639	21.713	7	2.77337e-12	0.000	5.91698e-12
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	1011071 3437639	41.660	13	4.03382e-6	0.000	8.50212e-6
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.380	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.760	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.519	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.038	-	-
2022-12-08	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.71	-	-
2022-12-08	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.42	-	-
2022-12-08	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	36.95	-	-

ECM factoring results:

Total ECM effort:	12.644 GHz-days
Estimated T-Level:	30.759

Digits	B1	Complete	FacMiss
20	11000	82.656	0.000%
25	50000	12.973	0.000%
30	250000	1.550	21.221%
35	1000000	0.152	85.907%
40	3000000	0.013	98.739%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	0.652
250000	25000000		585	6.791
1000000	100000000		111	5.154
1000000	100000000	2689135741713702483793673788961	1	0.046

	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
2017-02-16	kkmrkkblmbrbk	kel1	250000	25000000						585	6.791
2019-01-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-01	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-07	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-13	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-19	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-25	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-03	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-13	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-21	storm5510	3570_Ivy_Bridge	1000000	100000000						3	0.139
2019-03-27	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-03	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-09	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-17	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-26	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-03	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-11	Niels_Mache_Nextcloud	SuperDry-JP	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
2019-06-10	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-21	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-10	Niels_Mache_Nextcloud		1000000	100000000						3	0.139
2019-07-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-03	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-10	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-17	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000	2689135741713702483793673788961	101.085	1	2	3123371253132382	1	0.046
2019-08-20	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-27	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-03	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-11	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-18	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-26	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-03	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-10	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-18	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-25	Niels_Mache_Nextcloud	SuperDry3	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 M101107

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Ollaptop

1011071

3437639

13677629613203393

11514506E66AB6__

2017-09-21

Oliver Kruse

Manual testing

1011071

3437639

13677629613203393

11514506E66AB6__

2017-09-22

Oliver Kruse

Manual testing

1011071

3437639

13677629613203393

11514506E66AB6__

2017-11-06

kkmrkkblmbrbk

c4.xlarge

1011071

3437639

13677629613203393

11514506E66AB6__

2019-08-18

AN0NYM0US

dory

1011071

3437639

13677629613203393

2689135741713702483793673788961

EBCCDAF1971AF25C

2019-08-18

Niels_Mache_Nextcloud

SuperDry-X

1011071

3437639

13677629613203393

2689135741713702483793673788961

EBCCDAF1971AF25C

2022-04-15

LordJulius

WhiteBox

1011071

3437639

13677629613203393

2689135741713702483793673788961

EBCCDAF1971AF25C

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 = 6567654483390 (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:

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

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