A359120 Number of primes p with 10^(n-1) < p < 10^n such that 10^n-p is also prime.

3, 11, 47, 221, 1433, 9579, 69044, 519260, 4056919, 32504975, 266490184, 2224590493, 18850792161

Offset: 1

Author

N. J. A. Sloane, Dec 17 2022

Keywords

• nonn
• more

Comments

The terms of A358310 come in decreasing blocks; a(n) is the length of the n-th block.

Examples

			For n = 1, there are three primes p with 1 < p < 10 such that 10-p is also prime, 3, 5, and 7, so a(1) = 3.
		

Crossrefs

A107318 and A065577 are very similar.

Cf. A006879, A358310.

Programs

PARI

a(n) = {if(n==1,return(3)); my(res=0, pow10=10^n); forprime(p=2, 10^(n-1), if(isprime(pow10-p), res++)); forprime(p=10^(n-1), pow10>>1, if(isprime(pow10-p), res+=2)); res} \\ David A. Corneth, Dec 17 2022

Python

from sympy import isprime, primerange
def a(n):
    lb, ub = 10**(n-1), 10**n
    s1 = sum(1 for p in primerange(1, lb) if isprime(ub-p))
    s2 = sum(2 for p in primerange(lb, 5*lb) if isprime(ub-p))
    return s1 + s2 + int(n == 1)
print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Dec 17 2022

Extensions

a(7)-a(9) from Michael S. Branicky, Dec 17 2022

a(10)-a(11) from David A. Corneth, Dec 17 2022

a(12) from N. J. A. Sloane, Dec 17 2022, found using Corneth's PARI program.

a(13) from Martin Ehrenstein, Dec 18 2022, found using Walisch's primesieve library.