A057678 Primes of the form 2^p - p where p is prime.

2, 5, 8179, 524269

Offset: 1

Author

Labos Elemer, Oct 19 2000

Keywords

• nonn
• more

Comments

Next term, if it exists, has more than 618 digits. - Emeric Deutsch, Mar 27 2005

Next term, if it exists, has more than 10,000 digits.

The corresponding primes p are: 2, 3, 13, 19, .... - Gerasimov Sergey, Jul 26 2013

The corresponding 2^p - 1 are 3, 7, 8191, 524287 which are Mersenne primes (A000668). Is this the case for all members of the sequence? None of the other Mersenne primes < 2^132049-1 correspond to members of the sequence. - Robert Israel, Jul 18 2016

Next term is 2^481801-481801. 2^481801-1 is not a Mersenne prime. - Joerg Arndt, Jul 19 2016

Examples

			p=3 is prime, and so is 2^p - p = 8 - 3 = 5, so 5 is in the sequence. - _Michael B. Porter_, Jul 19 2016
		

Crossrefs

Cf. A000668, A057663, A057664, A057665, A056677.

Programs

Maple

a:=proc(n) if isprime(2^ithprime(n)-ithprime(n))=true then 2^ithprime(n)-ithprime(n) else fi end: seq(a(n),n=1..310); # Emeric Deutsch

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[p=2^p-p],AppendTo[lst,p]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 28 2009 *)
Select[Table[2^p-p,{p,Prime[Range[20]]}],PrimeQ] (* Harvey P. Dale, Sep 20 2018 *)