Prime Numbers Embedded in Digits of Pi

Theorem

The sequence of prime numbers that can be found starting from the beginning of the decimal expansion of $\pi$ (pi) begins:

$3, 31, 314 \, 159, 31 \, 415 \, 926 \, 535 \, 897 \, 932 \, 384 \, 626 \, 433 \, 832 \, 795 \, 028 \, 841, \ldots$

This sequence is A005042 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Proof

By inspection.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $314,159$