10 313 Exponent Status

Great Internet Mersenne Prime Search
GIMPS
Finding World Record Primes Since 1996

PrimeNet Exponent Status

M_n

Details

Composite, with 2 known prime factors. Cofactor is composite.

Trial Factored to 2⁶⁸

TF target 2⁴⁴

Factored

Factor	Digits	Bits	Date
1924418111160065167	19	60.7	old
1088136278280840662986480518790127	34	109.7	2010-02-19 11:44:00

P-1 factors

Date	Factors	B1	B2
2022-10-22	No new factors discovered	100000000000	120170262311539440

ECM

Digits	B1	Curves
25	50000	280 / 280
30	250000	640 / 640
35	1000000	1566 / 1566
40	3000000	4588 / 4588
45	11000000	9201 / 9201
50	44000000	3287 / 16550

Estimated T-Level: 46.0 ⓘ

TF below 2^148 is very unlikely to find new factors due to ECM effort.

Status	Proof	Date	User	Residue	Number of known factors	Shift	Type	Base
Verified	No proof (small exponent)	2017-09-21	Oliver Kruse	EA02181FD8A3F58B	2	0	1	3
Verified	No proof (small exponent)	2017-10-02	kkmrkkblmbrbk	EA02181FD8A3F58B	2	0	1	3
Verified	No proof (small exponent)	2017-10-12	kkmrkkblmbrbk	EA02181FD8A3F58B	2	4122	1	3
Verified	No proof (small exponent)	2020-04-17	Oliver Kruse	75EBC7937EC95A87	2	9219	5	3
Verified	No proof (small exponent)	2024-07-01	kkmrkkblmbrbk	75EBC7937EC95A87	2	7780	5	3

History

Date	User	Type	Result
2025-02-27	masser	NF-PP1	Start=90/41, B1=640000000, B2=639360000000
2025-02-18	masser	NF-PP1	Start=6/5, B1=640000000, B2=639360000000
2025-01-30	masser	NF-PP1	Start=2/7, B1=640000000, B2=639360000000
2024-07-01	kkmrkkblmbrbk	C-PRP	M10313/1088136278280840662986480518790127/1924418111160065167 : 75EBC7937EC95A87
2022-10-22	Anton Repko	F-PM1	Factor: 1924418111160065167 / B1=100000000000, B2=120170262311539440
2021-08-01	ViliamF	NF-PM1	B1=250000000, B2=40250000000
2020-04-17	Oliver Kruse	C-PRP	M10313/1924418111160065167/1088136278280840662986480518790127 : 75EBC7937EC95A87
2017-10-12	kkmrkkblmbrbk	C-PRP	M10313/1924418111160065167/1088136278280840662986480518790127 : EA02181FD8A3F58B
2017-10-02	kkmrkkblmbrbk	C-PRP	M10313/1924418111160065167/1088136278280840662986480518790127 : EA02181FD8A3F58B
2017-09-21	Oliver Kruse	C-PRP	M10313/1924418111160065167/1088136278280840662986480518790127 : EA02181FD8A3F58B
2016-09-07	kkmrkkblmbrbk	NF-PM1	B1=100000000, B2=10000000000, E=12
2010-02-19	Matthias Wurtinger	F-ECM	Factor: 1088136278280840662986480518790127