A pi-prime is a prime number appearing in the decimal expansion of pi. The known examples are 3, 31, 314159, 31415926535897932384626433832795028841, ... (Sloane's A005042). The numbers of digits in these examples are 1, 2, 6, 38, 16208, 47577, 78073, ... (Sloane's A060421). The largest of these were found by E. W. Weisstein on Apr. 1, 2006 and Jul. 13, 2006, respectively. There are no others with (E. W. Weisstein, Jul. 17, 2006).

Another set of pi-related primes is the positive integers such that is prime, where is the floor function. The first few are 1, 3, 4, 12, 73, 317, 2728, 6826, 7683, 7950, 14417, ... (Sloane's A059792), corresponding to the primes 3, 31, 97, 924269, ... (Sloane's A077547).

Similarly, the first few such that is prime, where is the ceiling function are 5, 29, 88, 948, 1071, 1100, 1578, ... (Sloane's A111937) with no others less than , corresponding to the primes 307, 261424513284461, 56129192858827520816193436882886842322337671, ... (Sloane's A118843).

Brown, K. S. "Primes in the Decimal Expansion of Pi." http://www.sixfingeredman.net/ref/mathpages-notes/kmath184/kmath184.htm.

Prime Curios! "314159." http://primes.utm.edu/curios/page.php?short=314159.

Sloane, N. J. A. Sequences A005042/M3129, A059792, A077547, A060421, A111937, and A118843 in "The On-Line Encyclopedia of Integer Sequences."

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Weisstein, Eric W. "Pi-Prime." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Pi-Prime.html