13 313 Exponent Status

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

PrimeNet Exponent Status

M_n

Details

Composite, with 4 known prime factors. Cofactor is composite.

Trial Factored to 2⁶⁸

TF target 2⁴⁴

Factored

Factor	Digits	Bits	Date
1065041	7	20.0	old
4420971488413651020242287325891330210985806927	46	151.6	2025-08-02 01:00:32
158187906136879413178423727756400738806449925167	48	156.8	2025-08-02 01:01:02
196141090224244013324472146788722286414906358209	48	157.1	2025-08-03 14:50:43

ECM

Digits	B1	Curves
25	50000	280 / 280
30	250000	640 / 640
35	1000000	1566 / 1566
40	3000000	4588 / 4588
45	11000000	1604 / 9201

Estimated T-Level: 40.9 ⓘ

TF below 2^131 is very unlikely to find new factors due to ECM effort.

Status	Proof	Date	User	Residue	Number of known factors	Shift	Type	Base
Factored	No proof (small exponent)	2017-09-21	Oliver Kruse	2BD2B76138E6A0C7	1	0	1	3
Factored	No proof (small exponent)	2017-10-12	kkmrkkblmbrbk	2BD2B76138E6A0C7	1	489	1	3
Factored	No proof (small exponent)	2020-04-17	Oliver Kruse	86E3677A07CCEA06	1	10258	5	3
Factored	No proof (small exponent)	2024-07-01	kkmrkkblmbrbk	86E3677A07CCEA06	1	13183	5	3
Verified	No proof (small exponent)	2025-08-08	Elysia	86E3677A07CCEA06	4	5502	5	3

History

Date	User	Type	Result
2025-08-08	Elysia	C-PRP	M13313/1065041/4420971488413651020242287325891330210985806927/158187906136879413178423727756400738806449925167/196141090224244013324472146788722286414906358209 : 86E3677A07CCEA06
2025-08-03	Ryan Propper	F-ECM	Factor: 196141090224244013324472146788722286414906358209
2025-08-02	Ryan Propper	F-ECM	Factor: 158187906136879413178423727756400738806449925167
2025-08-02	Ryan Propper	F-ECM	Factor: 4420971488413651020242287325891330210985806927
2025-02-27	masser	NF-PP1	Start=173/31, B1=430000000, B2=429570000000
2025-02-02	masser	NF-PP1	Start=2/7, B1=430000000, B2=429570000000
2025-01-30	masser	NF-PP1	Start=6/5, B1=430000000, B2=429570000000
2024-07-01	kkmrkkblmbrbk	C-PRP	M13313/1065041 : 86E3677A07CCEA06
2023-12-19	-anonymous-	NF-PM1	B1=100000000000, B2=122154521813133810
2023-05-18	JacobZ	NF-PM1	B1=8300000000, B2=34023579430740900
2022-02-05	Joss	NF-PM1	B1=1000000, B2=3910366209750
2020-04-17	Oliver Kruse	C-PRP	M13313/1065041 : 86E3677A07CCEA06
2017-10-12	kkmrkkblmbrbk	C-PRP	M13313/1065041 : 2BD2B76138E6A0C7
2017-09-21	Oliver Kruse	C-PRP	M13313/1065041 : 2BD2B76138E6A0C7
2017-09-21	Oliver Kruse	C-PRP	M13313/1065041 : 2BD2B76138E6A0C7