Small Mersenne Prime Factors (page 487/5610)

Small Mersenne Prime Factors
Prime numbers of the form M_p= 2^p − 1 are called Mersenne primes. For M_p to be prime, p must also be prime.
Any factor q of a Mersenne number 2^p − 1 must be of the form 2kp + 1, where integer k ≥ 0. Furthermore, q must be 1 or 7 mod 8.

Exp.	Prime Factor	Digits	Year
2785697	22285577	8	~1983
2785703	5571407	7	~1981
2785751	133716049	9	~1985
2785847	66860329	8	~1984
2785873	16715239	8	~1982
2785907	22287257	8	~1983
2785963	44575409	8	~1984
2785973	66863353	8	~1984
2785997	16715983	8	~1982
2786009	39004127	8	~1983
2786153	156024569	9	~1985
2786219	5572439	7	~1981
2786411	5572823	7	~1981
2786491	117032623	9	~1985
2786561	89169953	8	~1984
2786579	5573159	7	~1981
2786669	83600071	8	~1984
2786681	133760689	9	~1985
2786909	89181089	8	~1984
2787017	16722103	8	~1983
2787017	22296137	8
2787019	4665469807	10	~1988
2787299	50171383	8	~1984
2787409	83622271	8	~1984
2787443	5574887	7	~1981

Exp.	Prime Factor	Digits	Year
2787461	16724767	8	~1983
2787503	5575007	7	~1981
2787503	72475079	8
2787557	16725343	8	~1983
2787557	22300457	8
2787769	66906457	8	~1984
2787977	16727863	8	~1983
2788199	5576399	7	~1981
2788301	22306409	8	~1983
2788531	27885311	8	~1983
2788619	5577239	7	~1981
2788619	22308953	8
2788627	50195287	8	~1984
2788829	66931897	8	~1984
2788979	5577959	7	~1981
2789063	5578127	7	~1981
2789117	16734703	8	~1983
2789459	357050753	9	~1986
2789477	22315817	8	~1983
2789483	66947593	8	~1984
2789729	22317833	8	~1983
2789777	16738663	8	~1983
2789939	5579879	7	~1981
2790209	39062927	8	~1983
2790311	72548087	8	~1984

Exp.	Prime Factor	Digits	Year
2790421	16742527	8	~1983
2790497	16742983	8	~1983
2790647	72556823	8	~1984
2790883	27908831	8	~1983
2791093	16746559	8	~1983
2791109	39075527	8	~1983
2791469	22331753	8	~1983
2791549	111661961	9	~1985
2791559	5583119	7	~1981
2791561	61414343	8	~1984
2791783	27917831	8	~1983
2791799	50252383	8	~1984
2791837	16751023	8	~1983
2791849	61420679	8	~1984
2791963	67007113	8	~1984
2791979	5583959	7	~1981
2792099	5584199	7	~1981
2792171	5584343	7	~1981
2792249	22337993	8	~1983
2792261	22338089	8	~1983
2792351	5584703	7	~1981
2792423	5584847	7	~1981
2792423	89357537	8
2792459	22339673	8	~1983
2792617	16755703	8	~1983

Exp.	Prime Factor	Digits	Year
2792711	5585423	7	~1981
2792717	67025209	8	~1984
2792767	27927671	8	~1983
2792771	5585543	7	~1981
2792771	72612047	8
2792831	5585663	7	~1981
2792861	22342889	8	~1983
2792891	22343129	8	~1983
2792897	16757383	8	~1983
2793101	22344809	8	~1983
2793181	16759087	8	~1983
2793319	50279743	8	~1984
2793341	22346729	8	~1983
2793359	5586719	7	~1981
2793359	22346873	8
2793383	5586767	7	~1981
2793481	44695697	8	~1984
2793647	22349177	8	~1983
2793811	497298359	9	~1986
2793853	16763119	8	~1983
2793911	5587823	7	~1981
2794019	50292343	8	~1984
2794189	67060537	8	~1984
2794243	44707889	8	~1984
2794301	16765807	8	~1983

5.307.017 digits

26-01-11