23

This number is a prime.

Just showing those entries submitted by 'Das': (Click here to show all)

Kristen Eller ©2002

"Hilbert's problems" are a list of 23 problems put forth by David Hilbert in the year 1900. Note the number of words in the following quote attributed to him: "If I were to awaken after having slept for a thousand years, my first question would be: has the Riemann hypothesis been proven?" [Beedassy]

The smallest prime that is both preceded and followed by a prime number of successive composites. [Beedassy]

23! is the least factorial in which the digits 0 through 9 appear at least once. [Das]

23 is the largest row of Pascal's triangle all of whose entries are square-free (or 1). [Beedassy]

The number of characters in the interjection : "Yeah! Hints on the primes" (a most fitting anagram for "The Riemann Hypothesis" due to V. Rabin). [Beedassy]

The smallest prime p that divides the sum of the first p primes. [Beedassy]

There are exactly 23 prime-digit primes below one thousand, and 23 is one of them (more precisely the nth, where n is the (prime) sum of its digits). [Beedassy]

The smallest prime which when prefixed to the smallest pandigital string forms another prime: 230123456789. [Beedassy]

The first prime whose complexity is a prime smaller than itself (i.e., whose representation involving only addition, multiplication, brackets and 1's makes use of a smaller prime number of 1's): {(1+1)*(1+1+1)+1}*(1+1+1)+1+1. [Beedassy]

The smallest prime p such that a prime is formed both from the ordered and the reverse concatenations of the first noncomposites up to p: 123571113171923 ; 231917131175321. [Beedassy]

The smallest home prime for composite numbers. [Beedassy]

"PneumoVax 23" is the trade name for an anti-Streptococcus pneumoniae germ vaccine containing 23 of the most virulent and prevalent pneumococcal antigen serotypes. [Beedassy]

The largest prime p for which there exists a p-digit number with exactly p divisors. Can you find this 23-digit number? [Beedassy]