Call a number a prime string from the left if and all numbers obtained by successively removing the rightmost Digit are Prime. There are 83 left prime strings in base 10. The first few are 2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, ... (Sloane's A024770), the largest being 73,939,133. Similarly, call a number a prime string from the right if and all numbers obtained by successively removing the left-most Digit are Prime. The first few are 2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 103, 107, 113, 137, 167, 173, ... (Sloane's A033664). A large right prime string is 933,739,397.

**References**

Beeler, M.; Gosper, R. W.; and Schroeppel, R. *HAKMEM.* Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972.

Rivera, C. ``Problems & Puzzles (Puzzles): Prime Strings.'' http://www.sci.net.mx/~crivera/puzzles/puzz_002.htm.

Sloane, N. J. A. Sequence A024770 in ``The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.033664

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1999-05-26