M78647743 Mersenne number exponent details

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M78647743

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is 2 ^78647743 - 1

has 23675330 decimal digits

takes 245.419 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	0.3778	59.7015%	-	-	-	-	0.3778	59.7015%	0.0000%
PrimeNet	2⁷¹	6.0787	61.9718%	340000	16000000	5.3989	5.2360%	11.4776	63.9630%	1.9911%
GPU72	2⁷⁵	97.2934	64.0000%	500000	17000000	6.3299	3.7747%	103.6233	65.3589%	1.3589%
Difference	-8	-96.9156	-4.2985%	-500000	-17000000	-6.3299	-3.7747%	-103.2455	-5.6574%	-5.6574%

Known prime factors (3 factors, 134.5 bits, 0.00017105% known):

Remaining cofactor is PRP status unknown

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
78647743	1258363889	10	30.229	8 2³	-	8	8	1.822e-12	3.620e-5	7.367e-5
78647743	128092006069241	15	46.864	814340 2² × 5 × 19 × 2143	2008-09-29	19	2143	1.507e-7	0.0006	0.0010
78647743	194261900998599647	18	57.431	1235012561 47 × 26276863	2015-06-18	47	26276863	0.0004	6.4779	12.099

4 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
78647743	1258363889 128092006069241	161186354907101708038249	24	77.093
78647743	1258363889 194261900998599647	244452161225130835352947183	27	87.660
78647743	128092006069241 194261900998599647	24883396601734920262165920157927	32	104.295
78647743	1258363889 128092006069241 194261900998599647	31312367719288538408204006853192513898103	41	134.524

P-1 results:
No P-1 results for M78647743

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-29T07:21:00	markr	Manual testing	?	?	128092006069241	46.864	15	3.14757e-8	506.1	6.49096e-8
2015-06-18T11:51:00	TJAOI	Manual testing	2⁵⁷	2⁵⁸*	194261900998599647	57.431	18	0.000	506.1	0.000

ECM factoring results:
No ECM results for M78647743

Lucas-Lehmer results:
No L-L results for M78647743

PRP results:
No PRP results for M78647743

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

10⁰

10¹

10²

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2015-06-18T11:51:00+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