Small Mersenne Prime Factors (page 973/5490)

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
8789939	17579879	8	~1985
8789999	17579999	8	~1985
8790413	52742479	8	~1986
8790473	52742839	8	~1986
8790557	210973369	9	~1988
8790599	17581199	8	~1985
8790839	17581679	8	~1985
8791283	17582567	8	~1985
8791297	140660753	9	~1987
8791477	52748863	8	~1986
8791571	17583143	8	~1985
8791801	52750807	8	~1986
8791933	52751599	8	~1986
8792039	17584079	8	~1985
8792059	211009417	9	~1988
8792099	17584199	8	~1985
8792099	70336793	8
8792123	17584247	8	~1985
8792293	52753759	8	~1986
8792351	17584703	8	~1985
8792401	52754407	8	~1986
8792603	17585207	8	~1985
8792657	52755943	8	~1986
8792821	52756927	8	~1986
8792891	17585783	8	~1985

Exp.	Prime Factor	Digits	Year
8792963	17585927	8	~1985
8793041	52758247	8	~1986
8793149	70345193	8	~1987
8793193	52759159	8	~1986
8793227	70345817	8	~1987
8793397	140694353	9	~1987
8793431	369324103	9	~1988
8793439	87934391	8	~1987
8793479	70347833	8	~1987
8793671	17587343	8	~1985
8793839	70350713	8	~1987
8793871	351754841	9	~1988
8794267	422124817	9	~1989
8794501	52767007	8	~1986
8794561	52767367	8	~1986
8794613	52767679	8	~1986
8794631	17589263	8	~1985
8794757	334200767	9	~1988
8795327	158315887	9	~1988
8795431	158317759	9	~1988
8795483	17590967	8	~1985
8796001	193512023	9	~1988
8796253	211110073	9	~1988
8796503	17593007	8	~1985
8796581	70372649	8	~1987

Exp.	Prime Factor	Digits	Year
8796611	70372889	8	~1987
8796659	17593319	8	~1985
8796757	52780543	8	~1986
8796863	17593727	8	~1985
8796923	17593847	8	~1985
8797489	263924671	9	~1988
8797553	52785319	8	~1986
8797571	17595143	8	~1985
8797777	52786663	8	~1986
8798171	70385369	8	~1987
8798459	17596919	8	~1985
8798473	52790839	8	~1986
8798633	52791799	8	~1986
8798813	52792879	8	~1986
8799017	70392137	8	~1987
8799503	17599007	8	~1985
8799521	703961681	9	~1989
8799611	70396889	8	~1987
8799671	17599343	8	~1985
8799779	17599559	8	~1985
8799887	70399097	8	~1987
8799911	17599823	8	~1985
8799977	70399817	8	~1987
8799997	52799983	8	~1986
8800019	17600039	8	~1985

Exp.	Prime Factor	Digits	Year
8800523	17601047	8	~1985
8801129	70409033	8	~1987
8801329	1689855169	10	~1990
8801399	17602799	8	~1985
8801459	17602919	8	~1985
8801557	52809343	8	~1986
8801581	52809487	8	~1986
8801711	17603423	8	~1985
8801879	17603759	8	~1985
8802161	52812967	8	~1986
8802317	52813903	8	~1986
8802461	70419689	8	~1987
8802511	140840177	9	~1987
8802797	70422377	8	~1987
8802803	17605607	8	~1985
8802931	88029311	8	~1987
8803057	140848913	9	~1987
8803303	140852849	9	~1987
8803811	70430489	8	~1987
8803877	52823263	8	~1986
8804111	70432889	8	~1987
8804123	17608247	8	~1985
8804171	17608343	8	~1985
8804171	70433369	8
8804209	352168361	9	~1988

5.187.277 digits

25-11-17