13 309 Exponent Status

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

PrimeNet Exponent Status

M_n

Details

Composite, with 3 known prime factors. Cofactor is composite.

Trial Factored to 2⁶⁸

TF target 2⁴⁴

Factored

Factor	Digits	Bits	Date
121072138295586445748975622446567	33	106.6	2008-10-25 20:59:11
33277482213151028863942218094612687	35	114.7	old
35194344037697542355779819648716781562364121	44	144.7	2025-08-02 02:18:34

P-1 factors

Date	Factors	B1	B2
2023-12-19	No new factors discovered	100000000000	122154521813133808

ECM

Digits	B1	Curves
25	50000	280 / 280
30	250000	640 / 640
35	1000000	1566 / 1566
40	3000000	4588 / 4588
45	11000000	1586 / 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	B6C52AB6005A25C4	2	0	1	3
Factored	No proof (small exponent)	2017-10-02	kkmrkkblmbrbk	B6C52AB6005A25C4	2	0	1	3
Factored	No proof (small exponent)	2017-12-07	ATH	B6C52AB6005A25C4	2	8268	1	3
Factored	No proof (small exponent)	2020-04-17	Oliver Kruse	04CF9776ED90023F	2	5336	5	3
Factored	No proof (small exponent)	2024-07-01	kkmrkkblmbrbk	04CF9776ED90023F	2	11769	5	3
Verified	No proof (small exponent)	2025-08-07	ATH	04CF9776ED90023F	3	189	5	3

History

Date	User	Type	Result
2025-08-07	ATH	C-PRP	M13309/121072138295586445748975622446567/33277482213151028863942218094612687/35194344037697542355779819648716781562364121 : 04CF9776ED90023F
2025-08-02	Ryan Propper	F-ECM	Factor: 35194344037697542355779819648716781562364121
2025-02-27	masser	NF-PP1	Start=110/47, B1=430000000, B2=429570000000
2025-02-01	masser	NF-PP1	Start=2/7, B1=430000000, B2=429570000000
2025-01-29	masser	NF-PP1	Start=6/5, B1=430000000, B2=429570000000
2024-07-01	kkmrkkblmbrbk	C-PRP	M13309/121072138295586445748975622446567/33277482213151028863942218094612687 : 04CF9776ED90023F
2023-12-19	-anonymous-	F-PM1	Factor: 121072138295586445748975622446567 / 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	M13309/121072138295586445748975622446567/33277482213151028863942218094612687 : 04CF9776ED90023F
2017-12-07	ATH	C-PRP	M13309/121072138295586445748975622446567/33277482213151028863942218094612687 : B6C52AB6005A25C4
2017-10-02	kkmrkkblmbrbk	C-PRP	M13309/121072138295586445748975622446567/33277482213151028863942218094612687 : B6C52AB6005A25C4
2017-09-21	Oliver Kruse	C-PRP	M13309/33277482213151028863942218094612687/121072138295586445748975622446567 : B6C52AB6005A25C4
2008-10-25	Will Edgington	F-ECM	Factor: 121072138295586445748975622446567