M2 100 173 Mersenne number exponent details

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M2100173

<<<

>>>

is 2 ^2100173 - 1

has 632216 decimal digits

takes 0.138 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 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
Actual	2⁶⁷	14.1483	67.1642%	500000	15000000	0.1230	5.1532%	14.2713	68.8563%
Target	2⁶²	0.2925	64.5161%	10000	140000	0.0016	1.4513%	0.2942	65.0311%
Difference	+5	+13.8558	+2.6481%	+490000	+14860000	+0.1214	+3.7019%	+13.9771	+3.8252%

Known prime factors (1 factor, 41.0 bits, 0.00195314% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2100173	2228581777567	13	41.019	530571 3 × 176857	-	3	176857	2.570e-7	0.0009	0.0017

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 2228581777567	-	-	0.123	-	-	5.153%

Trial Factoring results:
No TF results for M2100173

ECM factoring results:

Total ECM effort:	5.350 GHz-days
Estimated T-Level:	20.954

Digits	B1	Complete	FacMiss
20	11000	2.084	12.439%
25	50000	0.191	82.630%
30	250000	0.012	98.805%

ECM Summary

B1	B2	curves	GHz-days
50000	50000	14	0.710
50000	5000000	13	1.106
50000	6711031	7	0.679
50000	6750000	7	0.681
50000	6837441	8	0.783
50000	7000000	7	0.693
50000	7113794	7	0.698

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-06	Oliver Kruse	ECM-HTC	50000	5000000						3	0.255
2019-08-29	MarkS	laptop64	50000	5000000						3	0.255
2021-10-08	happy5214	Focus	50000	6750000						7	0.681
2022-03-08	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.596
2022-06-06	JackBlock	school1	50000	50000						7	0.355
2022-06-11	debrouxl	dl380g9-1	50000	7113794						7	0.698
2022-08-19	Nesowa	6700T	50000	7000000						7	0.693
2022-10-24	JackBlock	school4	50000	50000						7	0.355
2022-10-26	debrouxl	o9020	50000	6711031						7	0.679
2023-01-18	debrouxl	o9020	50000	6837441						8	0.783

Lucas-Lehmer results:
No L-L results for M2100173

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07

Oliver Kruse

GTX-0

2228581777567

200FA6BDEE67D6__

2017-11-17

kkmrkkblmbrbk

c4.xlarge

2228581777567

200FA6BDEE67D6__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

this exponent TF target: 62

TF double-checked to: 67.7

ECM T-Level=20.95 ~= 53-bit

2⁵⁰

2⁶⁰

2⁷⁰

Last modified: 2023-01-18T19:34:52+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