A076106 Out of all the n-digit primes, which one takes the longest time to appear in the digits of Pi (ignoring the initial 3)? The answer is a(n), and it appears at position A076130(n).

7, 73, 373, 9337, 35569, 805289, 9271903

Offset: 1

Author

Jean-Christophe Colin (jc-colin(AT)wanadoo.fr), Oct 31 2002

Keywords

• hard
• more
• nonn
• base

Comments

a(8) requires > 1 billion digits of Pi. - Michael S. Branicky, Jul 08 2021

Examples

			Of all the 2-digit primes, 11 to 97, the last one to appear in Pi is 73, at position 299 (see A076130). - _N. J. A. Sloane_, Nov 28 2019
		

Links

• Carlos Rivera, Puzzle 40. The Pi Prime Search Puzzle (by Patrick De Geest), The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A000796, A047658, A076094, A076129, A076130.

Programs

Python

# download https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt, then
with open('pi-billion.txt', 'r') as f: digits_of_pi = f.readline()[2:]
# from sympy import S
# digits_of_pi = str(S.Pi.n(72*10**4))[2:] # alternate to loading data
from sympy import primerange
def A076106_A076130(n):
    global digits_of_pi
    bigp, bigloc = None, -1
    for p in primerange(10**(n-1), 10**n):
        loc = digits_of_pi.find(str(p))
        if loc == -1: print("not enough digits", n, p)
        if loc > bigloc:
            bigloc = loc
            bigp = p
    return (bigp, bigloc+1)
print([A076106_A076130(n)[0] for n in range(1, 6)]) # Michael S. Branicky, Jul 08 2021

Extensions

Definition clarified by N. J. A. Sloane, Nov 28 2019

a(7) from Michael S. Branicky, Jul 08 2021