Small Mersenne Prime Factors (page 905/6225)

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
7263143	14526287	8	~1985
7263287	58106297	8	~1986
7263419	14526839	8	~1985
7263611	58108889	8	~1986
7263673	43582039	8	~1986
7263787	72637871	8	~1986
7263863	14527727	8	~1985
7263983	14527967	8	~1985
7264193	43585159	8	~1986
7264277	101699879	9	~1987
7264319	14528639	8	~1985
7264381	43586287	8	~1986
7264391	14528783	8	~1985
7264643	14529287	8	~1985
7264841	58118729	8	~1986
7265003	14530007	8	~1985
7265207	188895383	9	~1987
7265339	14530679	8	~1985
7265381	58123049	8	~1986
7265603	14531207	8	~1985
7265663	14531327	8	~1985
7265701	43594207	8	~1986
7265759	14531519	8	~1985
7266073	43596439	8	~1986
7266101	43596607	8	~1986

Exp.	Prime Factor	Digits	Year
7266251	14532503	8	~1985
7266299	14532599	8	~1985
7266491	58131929	8	~1986
7266557	43599343	8	~1986
7266673	116266769	9	~1987
7266697	116267153	9	~1987
7266709	465069377	9	~1988
7266737	43600423	8	~1986
7266923	14533847	8	~1985
7266929	218007871	9	~1987
7267031	14534063	8	~1985
7267079	14534159	8	~1985
7267097	43602583	8	~1986
7267111	72671111	8	~1986
7267391	14534783	8	~1985
7267441	43604647	8	~1986
7267499	14534999	8	~1985
7267583	14535167	8	~1985
7267769	58142153	8	~1986
7268201	232582433	9	~1988
7268441	43610647	8	~1986
7268533	43611199	8	~1986
7268581	43611487	8	~1986
7268743	72687431	8	~1986
7268819	14537639	8	~1985

Exp.	Prime Factor	Digits	Year
7268881	1032181103	10	~1989
7269239	14538479	8	~1985
7269281	58154249	8	~1986
7269307	130847527	9	~1987
7269371	58154969	8	~1986
7269481	159928583	9	~1987
7269527	174468649	9	~1987
7269539	14539079	8	~1985
7269611	14539223	8	~1985
7269643	72696431	8	~1986
7269683	14539367	8	~1985
7269937	43619623	8	~1986
7269959	14539919	8	~1985
7270253	43621519	8	~1986
7270379	14540759	8	~1985
7270391	14540783	8	~1985
7270643	14541287	8	~1985
7270663	72706631	8	~1986
7270733	407161049	9	~1988
7270751	14541503	8	~1985
7271477	43628863	8	~1986
7271483	14542967	8	~1985
7271501	43629007	8	~1986
7271723	14543447	8	~1985
7271777	58174217	8	~1986

Exp.	Prime Factor	Digits	Year
7271963	14543927	8	~1985
7272007	479952463	9	~1988
7272227	58177817	8	~1986
7272337	43634023	8	~1986
7272431	58179449	8	~1986
7272751	72727511	8	~1986
7272911	14545823	8	~1985
7273061	43638367	8	~1986
7273463	14546927	8	~1985
7273583	14547167	8	~1985
7273633	43641799	8	~1986
7273633	1963880911	10
7273817	58190537	8	~1986
7274053	43644319	8	~1986
7274339	14548679	8	~1985
7274437	43646623	8	~1986
7274639	14549279	8	~1985
7274857	43649143	8	~1986
7275011	14550023	8	~1985
7275019	349200913	9	~1988
7275077	43650463	8	~1986
7275353	101854943	9	~1987
7275391	72753911	8	~1986
7275397	43652383	8	~1986
7275431	14550863	8	~1985

5.920.543 digits

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