right-truncatable primes
(another Prime Pages' Glossary entries)
The Prime Glossary
Glossary: Prime Pages: Top 5000: 73939133 is the largest prime for which all the initial segments of the decimal expansion are also prime (7, 73, 739, ...). So even if we stop writing before we finish the number, we have still written a prime! Such primes are called right-truncatable primes. (If we allow 1 to be considered a prime, then the largest are 1979339333 and 1979339339.)

These primes are also called by many other (deprecated) names. Card called them snowball primes in 1968 [Card1968]. Michael Stueben named them super-primes after reading Alf van der Poorten's note in 1985 (Math. Int. 7:2 (1985) 40). Walstrom and Berg in 1969 called them prime-primes [WB1969].

What if we change the base (radix) and again look for right truncatable primes? The following table gives the answer for the first few bases.

baselargest right-truncatable prime in this base
21011
32122
42333 (or 133313)
534222
62155555
725642 (or 166426)
82117717
93444224222

See Also: LeftTruncatablePrime, PermutablePrime, DeletablePrime

References:

AG1977
I. O. Angell and H. J. Godwin, "On truncatable primes," Math. Comp., 31 (1977) 265--267.  MR 55:248
Caldwell87
C. Caldwell, "Truncatable primes," J. Recreational Math., 19:1 (1987) 30--33. [A recreational note discussing left truncatable primes, right truncatable primes, and deletable primes.]
Card1968
Card, "Patterns in primes," J. Recreational Math., 1 (1968) 93--99.
WB1969
J. Walstrom and M. Berg, "Prime primes," Math. Mag., 42 (1969) 232.  MR0253974


Chris Caldwell © 1999-2008 (all rights reserved)