BASE 10 BASE 16

enzocreti · 2019-03-30, 08:49

2, 3, 9, 11, 87, 233, 477, 507, 785, 2313, 8967=j

these are the values I found with Pari

I explain with examples:

2^11-1=2047. If I enter 2047 in a base converter calculator from base 16 to base 10 I have a prime number=8263.

The same with 2^9-1=511 wreitten under base 16 to base 10 =1297 which is a prime

and the same with all other j's.

Do you think that the number of these j's is not infinite? And looking at the values of j which are primes: 2,3,11,233 I noticed that

2,3,11,233 are Chen prime, Sophie Germain Primes and they are prime p such that 6*p+1 is also prime.
Just coincidence?

2019-03-30, 08:49	#1
enzocreti Mar 2018 2×5×53 Posts	BASE 10 BASE 16 2, 3, 9, 11, 87, 233, 477, 507, 785, 2313, 8967=j these are the values I found with Pari I explain with examples: 2^11-1=2047. If I enter 2047 in a base converter calculator from base 16 to base 10 I have a prime number=8263. The same with 2^9-1=511 wreitten under base 16 to base 10 =1297 which is a prime and the same with all other j's. Do you think that the number of these j's is not infinite? And looking at the values of j which are primes: 2,3,11,233 I noticed that 2,3,11,233 are Chen prime, Sophie Germain Primes and they are prime p such that 6p+1 is also prime. Just coincidence? Last fiddled with by enzocreti on 2019-03-30 at 08:50*

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