Small Mersenne Prime Factors (page 855/5190)

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
7270379	14540759	8	~1985
7270391	14540783	8	~1985
7270643	14541287	8	~1985
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
7271963	14543927	8	~1985
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

Exp.	Prime Factor	Digits	Year
7274639	14549279	8	~1985
7274857	43649143	8	~1986
7275011	14550023	8	~1985
7275019	349200913	9	~1988
7275077	43650463	8	~1986
7275397	43652383	8	~1986
7275431	14550863	8	~1985
7275479	14550959	8	~1985
7275497	101856959	9	~1987
7275503	14551007	8	~1985
7275551	130959919	9	~1987
7275743	14551487	8	~1985
7276039	291041561	9	~1988
7276471	116423537	9	~1987
7276931	14553863	8	~1985
7277183	14554367	8	~1985
7277189	58217513	8	~1986
7277279	58218233	8	~1986
7277423	14554847	8	~1985
7277593	116441489	9	~1987
7277681	43666087	8	~1986
7277723	14555447	8	~1985
7277843	14555687	8	~1985
7278059	14556119	8	~1985
7278209	276571943	9	~1988

Exp.	Prime Factor	Digits	Year
7278239	131008303	9	~1987
7278253	43669519	8	~1986
7278599	14557199	8	~1985
7278599	232915169	9
7278613	43671679	8	~1986
7278857	43673143	8	~1986
7278917	43673503	8	~1986
7279199	14558399	8	~1985
7279241	43675447	8	~1986
7279253	43675519	8	~1986
7279333	43675999	8	~1986
7279439	14558879	8	~1985
7279763	14559527	8	~1985
7280137	43680823	8	~1986
7280183	14560367	8	~1985
7280549	58244393	8	~1986
7280579	14561159	8	~1985
7280731	131053159	9	~1987
7280737	43684423	8	~1986
7280831	14561663	8	~1985
7280951	14561903	8	~1985
7281077	43686463	8	~1986
7281203	14562407	8	~1985
7281247	72812471	8	~1986
7281277	43687663	8	~1986

Exp.	Prime Factor	Digits	Year
7282217	43693303	8	~1986
7282621	43695727	8	~1986
7282679	14565359	8	~1985
7282739	14565479	8	~1985
7282811	14565623	8	~1985
7282811	58262489	8
7282981	43697887	8	~1986
7283173	43699039	8	~1986
7283351	14566703	8	~1985
7283401	43700407	8	~1986
7283411	14566823	8	~1985
7283411	58267289	8
7283417	101967839	9	~1987
7283657	43701943	8	~1986
7283741	58269929	8	~1986
7283777	58270217	8	~1986
7283833	43702999	8	~1986
7283891	14567783	8	~1985
7283999	14567999	8	~1985
7284131	14568263	8	~1985
7284197	43705183	8	~1986
7284443	14568887	8	~1985
7284493	43706959	8	~1986
7284749	174833977	9	~1987
7284971	14569943	8	~1985

4.888.230 digits

25-06-29