mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Blogorrhea > sweety439

Reply
 
Thread Tools
Old 2020-10-24, 16:20   #1
sweety439
 
sweety439's Avatar
 
Nov 2016

26·3·13 Posts
Default 47 & 383

They are not only two primes of the form 3*2^n-1, but also ....

* They are the first two non-Sophie-Germain primes (i.e. primes p such that 2*p+1 is not prime) of the form 3*2^n-1

* They are the largest two numbers n such that the primary pretender of n (A000790) = n-1

* They are the largest two primes p such that the smallest pseudoprime base p (A090086) >= p-1

* They are both indices of the records for the smallest k such that n*2^k+1 is prime (47 gets 583, 383 gets 6393, both are >10 times of the previous record)

* They also have no easy prime of the form either 2*n^k+1 or n^k+2 (these two forms are dual) (for 47, they are 2*47^175+1 and 47^113+2, and there are no (probable) prime for both two forms for 383)
sweety439 is offline   Reply With Quote
Reply

Thread Tools


All times are UTC. The time now is 12:15.

Fri Nov 27 12:15:08 UTC 2020 up 78 days, 9:26, 4 users, load averages: 1.40, 1.28, 1.23

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.