M100 447 Mersenne number exponent details

is 2 ¹⁰⁰⁴⁴⁷ - 1

has 30238 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	295.8169	74.6269%	1000000000	6734439121410	1,185.3149	25.4892%	1,481.1317	81.0943%
Target	2⁴⁴	0.0000	61.3636%	1200	17000	0.0000	4.0815%	0.0000	62.9406%
Difference	+23	+295.8169	+13.2632%	+999998800	+6734439104410	+1,185.3149	+21.4077%	+1,481.1317	+18.1537%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100447	705322762481	12	39.359	3510920 2³ × 5 × 7 × 12539	-	8	12539	1.414e-6	2.226e-6	4.112e-6
100447	10833463432273607	17	53.266	53926266749 229 × 235485881	2010-01-28	229	235485881	0.0133	0.0413	0.0772

exponent	prime factors	composite factor	digits	bits*
100447	705322762481 10833463432273607	7641088355288116339866138967	28	92.626

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: 705322762481 skipped known factor: 10833463432273607	-	-	0.656	-	-	11.727%
2021-12-17	Seth_Tr	Manual testing	1000000000	6734439121410		-	skipped known factor: 705322762481 skipped known factor: 10833463432273607	-	-	1,185	-	-	25.489%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2022-04-09	LordJulius	Manual testing	2¹	2⁵⁷	10833463432273607	53.266	17	0.013	0.000	0.027
2022-04-09	LordJulius	Manual testing	2¹	2⁵⁷	705322762481	39.359	12	1.41404e-6	0.000	3.00872e-6
2022-04-09	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.191	-	-
2022-04-09	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.382	-	-
2022-04-09	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.765	-	-
2022-04-09	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.529	-	-
2022-04-09	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.058	-	-
2022-04-09	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.77	-	-
2022-04-09	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.55	-	-
2022-10-13	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	37.20	-	-
2022-10-13	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	74.39	-	-
2022-10-13	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	148.8	-	-

ECM factoring results:

Total ECM effort:	12.733 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
		10833463432273607	1	0.00000e+0
50000	5000000		280	0.650
250000	25000000		585	6.790
1000000	100000000		114	5.293

	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
2010-01-28	Rob_Dee	twopc			10833463432273607	53.266		1		1	-
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2014-04-11	TJAOI	Manual testing	50000	5000000						40	0.093
2014-05-08	TJAOI	Manual testing	50000	5000000						231	0.536
2017-01-20	kkmrkkblmbrbk	kel1	250000	25000000						585	6.790
2019-01-24	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-01-29	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-04	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-10	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-22	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-01	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-06	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-11	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-17	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-31	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-06	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-12	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-23	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-29	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-05-07	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-14	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-04	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-15	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-22	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-07-30	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-06	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-13	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-20	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-08-28	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-19	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-03	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-18	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-26	Niels_Mache_Nextcloud	SuperDry-Y	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 M100447

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

705322762481

10833463432273607

16EBCF848BE3AA__

2017-09-21

Oliver Kruse

Manual testing

705322762481

10833463432273607

16EBCF848BE3AA__

2017-09-22

Oliver Kruse

Manual testing

705322762481

10833463432273607

16EBCF848BE3AA__

2017-11-06

kkmrkkblmbrbk

c4.xlarge

705322762481

10833463432273607

16EBCF848BE3AA__

2020-04-17

Oliver Kruse

AddPrpType5

705322762481

10833463432273607

192F1D52B3F0C8__

2022-04-15

LordJulius

WhiteBox

705322762481

10833463432273607

192F1D52B3F0C884

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)

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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

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