Number Gossip

Enter a number and it will tell you everything you wanted to know about the number but were afraid to ask.

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I first used my old h.s. football number:

* The 61st Fibonacci number (2504730781961) is the smallest Fibonacci number which contains all the digits from 0 to 9
* 61 is the smallest multidigit prime p such that the sum of digits of pp is a square
* 61 is the smallest prime whose reversal is a square

I like the number 23:

# 23 is the smallest group of people where there is more than a 50% chance that 2 people will share the same birthday (day and month, not year)
# 23 is the smallest isolated prime, i.e., not an element of a set of twin primes
# 23 is the smallest prime whose reversal is a power: 32 = 25
# 23 is the only prime p such that p! is p digits long
# 23 is the least pandigital factorial, that is it contains all the digits 0 through 9 at least once
# 23 is the smallest prime p such that the ring of integers in the cyclotomic field of pth roots of unity does not have unique factorization

Believe it or not, but I knew that first bit of information (about the birthdays), having read it in an old "bar tricks" book I used to have. The rest of it, though....

Number Gossip