
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) 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 righttruncatable 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 superprimes after reading Alf van der Poorten's note in 1985 (Math. Int. 7:2 (1985) 40). Walstrom and Berg in 1969 called them primeprimes [WB1969]. Righttruncatable primes for which there is no further possible extension have been called superprime leaders. 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, as well as the tally of righttruncatable primes, and of superprime leaders.
As the base increases, there are more opportunities for finding extensions from each prime; therefore, heuristically, the number of righttruncatable primes would be expected to increase without bound as the base increases. Similarly, the number of superprime leaders also would be expected to increase without bound. For example, for base 42, there are 175734 primes and 63872 leaders.
See Also: LeftTruncatablePrime, PermutablePrime, DeletablePrime Related pages (outside of this work) References:
Chris K. Caldwell © 19992019 (all rights reserved)
