A104841 The first n-digit prime occurring in the decimal expansion of Pi, A000796.

3, 31, 653, 4159, 14159, 314159, 1592653, 28841971, 795028841, 5926535897, 93238462643, 141592653589, 9265358979323, 23846264338327, 841971693993751, 8628034825342117, 89793238462643383, 348253421170679821, 3832795028841971693, 89793238462643383279

Offset: 1

Author

Zak Seidov, Mar 27 2005

Keywords

• nonn
• base

Comments

For the next n-digit primes, see the b-file (link).

Sequence A198344 gives the position of these primes withing the digits of Pi.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1000 (terms 1..162 from M. F. Hasler)

Crossrefs

Cf. A104819 - A104842.

Cf. A000796, A198344.

Programs

PARI

default(realprecision,2000); A104841(n)={for( c=0, default(realprecision)-n-2, Pi\.1^c%10 & ispseudoprime(p=Pi\.1^(n+c-1)%10^n) & return(p));error("Please increase default(realprecision) to calculate A104841("n").")}  \\ M. F. Hasler, Oct 23 2011

Python

from sympy import S, isprime
pi = "3"+str(S.Pi.n(10**5))[2:] # or load data from file
def A104841_A198344(n): return next(((p, i+1) for i in range(len(pi)-n) if pi[i]!="0" and isprime(p:=int(pi[i:i+n]))), "not enough digits")
print([A104841_A198344(n)[0] for n in range(1, 21)]) # Michael S. Branicky, Dec 28 2022