M100 669 Mersenne number exponent details

is 2 ¹⁰⁰⁶⁶⁹ - 1

has 30305 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	295.1645	74.6269%	1000000000	6734439121410	1,185.3149	25.4918%	1,480.4794	81.0949%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1535%	0.0000	62.9684%
Difference	+23	+295.1645	+13.2632%	+999998800	+6734439103410	+1,185.3149	+21.3383%	+1,480.4794	+18.1266%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100669	158565553943	12	37.206	787559 17 × 46327	-	17	46327	2.669e-7	8.185e-6	1.519e-5
100669	1054679912047664423	19	59.872	5238354965519 13 × 5471 × 73652053	2010-02-18	5471	73652053	0.8618	0.0129	0.0241
100669	36217175160988200615222392311	29	94.871	179882462133269430585495 3 × 5 × 701 × 255971 × 66832665296623	2017-01-29	255971	66832665296623	5.033e+10	11,733	21,914

exponent	prime factors	composite factor	digits	bits*
100669	158565553943 1054679912047664423	167235904486392428652368469889	30	97.078
100669	158565553943 36217175160988200615222392311	5742796441652754233839552034931378932273	40	132.077
100669	1054679912047664423 36217175160988200615222392311	38197527113405892014639533275127776978183451553	47	154.742
100669	158565553943 1054679912047664423 36217175160988200615222392311	60568120459899670487013578592376169806518216213771 48623479	58	191.948

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: 158565553943 skipped known factor: 1054679912047664423	-	-	0.656	-	-	11.729%
2021-12-18	Seth_Tr	Manual testing	1000000000	6734439121410		-	skipped known factor: 158565553943 skipped known factor: 1054679912047664423	-	-	1,185	-	-	25.492%

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	2⁵³	2⁵⁷		-	-	0.179	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	158565553943	37.206	12	2.66871e-7	0.000	5.69211e-7
2018-11-01	J.R. Allen	Manual testing	2⁵⁷	2⁵⁸		-	-	0.191	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.191	-	-
2018-11-01	J.R. Allen	Manual testing	2⁵⁸	2⁵⁹		-	-	0.381	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.381	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰	1054679912047664423	59.872	19	0.099	0.000	0.201
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.526	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.051	-	-
2022-10-24	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.75	-	-
2022-10-24	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.50	-	-
2022-10-24	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	37.12	-	-
2022-10-24	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	74.23	-	-
2022-10-24	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	148.5	-	-

ECM factoring results:

Total ECM effort:	12.734 GHz-days
Estimated T-Level:	30.766

Digits	B1	Complete	FacMiss
20	11000	82.951	0.000%
25	50000	13.036	0.000%
30	250000	1.560	21.008%
35	1000000	0.153	85.798%
40	3000000	0.013	98.726%

ECM Summary

B1	B2	factor	curves	GHz-days
		1054679912047664423	1	0.00000e+0
50000	5000000		280	0.650
250000	25000000		366	4.248
250000	25000000	36217175160988200615222392311	219	2.542
1000000	100000000		114	5.293

ECM Details

										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
2010-02-09	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-09	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-09	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-09	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-09	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-09	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-10	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-10	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-10	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-11	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-11	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-11	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-12	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-12	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-12	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-13	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-13	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-13	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-13	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-13	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-14	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-14	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-14	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-14	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-14	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-16	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-16	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-16	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-17	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-17	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-17	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-17	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-18	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-18	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-18	Rob_Dee	twopc			1054679912047664423	59.872		1		1	-
2010-02-18	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-18	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-19	Rob_Dee	twopc	50000	5000000						1	0.002
2010-04-19	James Hintz	NEW_OMFG	50000	5000000						11	0.026
2014-06-19	TJAOI	Manual testing	50000	5000000						230	0.534
2017-01-29	kkmrkkblmbrbk	kel1	250000	25000000	36217175160988200615222392311	94.871	219	2		219	2.542
2017-01-29	kkmrkkblmbrbk	kel1	250000	25000000						366	4.248
2019-01-24	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-01-30	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-05	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-11	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-17	Niels_Mache_Nextcloud	SuperDry-JP	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-JP	1000000	100000000						3	0.139
2019-03-07	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-12	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-19	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-01	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-07	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-14	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-01	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-15	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-06	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-17	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-28	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-07-31	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-07	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-14	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-22	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-29	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-05	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-13	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-20	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-28	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-05	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-12	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-20	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-27	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-03	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-10	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M100669

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Ollaptop

158565553943

1054679912047664423

36217175160988200615222392311

0C8CD1F687CFA213

2017-09-21

Oliver Kruse

Manual testing

158565553943

1054679912047664423

36217175160988200615222392311

0C8CD1F687CFA213

2017-09-22

Oliver Kruse

Manual testing

158565553943

1054679912047664423

36217175160988200615222392311

0C8CD1F687CFA213

2017-11-06

kkmrkkblmbrbk

c4.xlarge

158565553943

1054679912047664423

36217175160988200615222392311

0C8CD1F687CFA2__

2020-04-17

Oliver Kruse

AddPrpType5

158565553943

1054679912047664423

36217175160988200615222392311

3D8FE13C46EF5D__

2022-04-15

LordJulius

WhiteBox

158565553943

1054679912047664423

36217175160988200615222392311

3D8FE13C46EF5D7E

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 = 6734439121410 (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

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=30.77 ~= 86-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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