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Old 2020-02-15, 04:06   #2
ewmayer's Avatar
Sep 2002
Rep├║blica de California

100110011000102 Posts

@tuckertao: It would help if you explained how you chose/found the above pair, and why you think it is somehow special. You have a large-ish smooth part in form of 2^191*3^90, then the largest-known Mersenne prime exponent, but I see nothing special about the remaining multiplier 40463441610*232792560 = 9419588158802421600. If I define a = 2^191*3^90*82589933, set n to your -prime, then successively increment n by a, I can easily find the next-larger pair of this form,
n = 21310867332998259383016283883353020788678719772398547918516685244168507150940923363729663389961621332915816701945558484016693248+-1
 = 2^191*3^90*82589933*9419588158802425428+-1 = 2^193*3^91*82589933*11*29*89*27648398432609+-1.
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