A137443 First n-digit prime in consecutive digits of e.

7, 71, 281, 4523, 74713, 904523, 6028747, 72407663, 360287471, 7427466391, 75724709369, 749669676277, 8284590452353, 99959574966967, 724709369995957, 2470936999595749, 28459045235360287, 571382178525166427

Offset: 1

Author

Dan Drake, Apr 18 2008

Keywords

• base
• nonn

Comments

If the "2" at the beginning of e is included, the only values for n <= 1000 that change are a(1) = 2, a(3) = 271 and a(85) = 2718281828459045235360287471352662497757247093699959574966967627724076630353547594571.

For another version starting with 2 see A095935. - Omar E. Pol, Oct 24 2011

Examples

			7427466391 is the first 10-digit prime found in consecutive digits of e, so a(10) = 7427466391.
		

Links

• Dan Drake, Table of n, a(n) for n = 1..1000
• Pegg, E. Jr. and Weisstein, E. W. Mathematica's Google Aptitude. MathWorld Headline news, Oct 13, 2004.

Crossrefs

Cf. A095926.

Cf. A001113, A095935. - Omar E. Pol, Oct 24 2011

Programs

Sage

def a(digits):
    bits = 0
    pos = 0
    while True:
        bits += (digits * 4) + 50
        decimals = RealField(bits, rnd='RNDZ')(exp(1)).frac().str()[2:]
        for s in range(pos, len(decimals) - digits + 1):
            if decimals[s] != '0':
                i = Integer(decimals[s:s+digits])
                if i.is_prime():
                    return i
        pos = len(decimals) - digits + 1