13 679 Exponent Status

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

PrimeNet Exponent Status

M_n

Details

Composite, with 6 known prime factors. Cofactor is composite.

Trial Factored to 2⁶⁸

TF target 2⁴⁴

Factored

Factor	Digits	Bits	Date
109433	6	16.7	old
246223	6	17.9	2008-08-26 19:58:40
100157639	9	26.6	2008-08-26 19:58:40
312975521	9	28.2	2008-08-26 19:58:40
19705922417816082121	20	64.1	2008-08-29 02:24:33
1295445979368162725657872910907040893208969	43	139.9	2023-06-09 08:20:34

P-1 factors

Date	Factors	B1	B2
2024-01-29	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	1556 / 9201

Estimated T-Level: 40.8 ⓘ

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	A499E92412B30409	5	0	1	3
Factored	No proof (small exponent)	2017-10-02	kkmrkkblmbrbk	A499E92412B30409	5	0	1	3
Factored	No proof (small exponent)	2017-12-07	ATH	A499E92412B30409	5	7785	1	3
Factored	No proof (small exponent)	2020-04-17	Oliver Kruse	A2D1D21DD345B30A	5	12055	5	3
Verified	No proof (small exponent)	2023-06-09	Denial140	A2D1D21DD345B30A	6	100	5	3

History

Date	User	Type	Result
2025-03-06	masser	NF-PP1	Start=118/11, B1=430000000, B2=429570000000
2025-02-11	masser	NF-PP1	Start=2/7, B1=430000000, B2=429570000000
2025-01-25	masser	NF-PP1	Start=6/5, B1=430000000, B2=429570000000
2024-01-29	Anton Repko	F-PM1	Factor: 19705922417816082121 / B1=100000000000, B2=122154521813133810
2023-06-09	Denial140	C-PRP	M13679/109433/246223/100157639/312975521/19705922417816082121/1295445979368162725657872910907040893208969 : A2D1D21DD345B30A
2023-06-09	Denial140	F-ECM	Factor: 1295445979368162725657872910907040893208969 / ECM curve 179, B1=3000000, B2=22972799850, Montgomery Sigma=2949510651080596
2023-05-20	JacobZ	NF-PM1	B1=8000000000, B2=35524619698317750
2022-03-04	Ethan O'Connor	NF-PM1	B1=1000000000, B2=248016220902450
2021-08-27	Seth_Tr	NF-PM1	B1=400000000
2020-04-17	Oliver Kruse	C-PRP	M13679/109433/246223/100157639/312975521/19705922417816082121 : A2D1D21DD345B30A
2017-12-07	ATH	C-PRP	M13679/109433/246223/100157639/312975521/19705922417816082121 : A499E92412B30409
2017-10-02	kkmrkkblmbrbk	C-PRP	M13679/109433/246223/100157639/312975521/19705922417816082121 : A499E92412B30409
2017-09-21	Oliver Kruse	C-PRP	M13679/109433/246223/100157639/312975521/19705922417816082121 : A499E92412B30409
2008-08-29	-anonymous-	F-ECM	Factor: 19705922417816082121
2008-08-26	-anonymous-	F	Factor: 312975521
2008-08-26	-anonymous-	F	Factor: 100157639
2008-08-26	-anonymous-	F	Factor: 246223