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113² = 12769 and its reversal 96721 = 311². [Friend]

The smallest three digit prime whose product and sum of digits is prime. [Russo]

Zu Chongzhi (or Tsu Ch'ung Chi), along with his son Zu Gengzhi, stated in a mathematical text entitled Zhui Shu (Method of Interpolation) that is approximately three hundred fifty-five divided by 113.

The smallest prime factor of 12345678910111213 (the concatenation of the first thirteen natural numbers). [Russo]

The Photoelectric Sieve, built by D. H. Lehmer in the 1930s, depended on prime numbers up to 113.

Ununtrium (atomic number 113) is the temporary name of a synthetic element that has the temporary symbol Uut. [Kulsha]

The Police (and general emergency) telephone number in Italy.

113 = 1 + (sum of first 13 odd primes - 13)/2. [Russo]

1^0+1^0+3^0=3;1^1+1^1+3^1=5;1^2+1^2+3^2=11;1^3+1^3+3^3=29;1^4+1^4+3^4=83; 113 is the smallest (non-trivial) prime for which the sums of the first 5 powers of the digits are all prime. [Rupinski]

The largest of the fifteen prime numbers p that require a prime number of digits when written in any prime base less than or equal to p. It is 1110001 in base 2, 11012 in base 3, 423 in base 5, 221 in base 7, and requires two digits in bases 11, 13, 17,... 113. [Hartley]

The three circularly permuted primes, i.e., 113, 131 and 311, can be concatenated in 3! different ways. After inserting a prime digit as a separator between these concatenated primes, the following four 11-digit primes can be obtained: 11371317311, 31151315113, 13153115113 and 11373117131. Note that the first two numbers are palindromic primes. [Necula]

The smallest prime of the form (p^2 + q^2 + r^2)/3, where p, q, r are 3 consecutive primes. [Pfoertner]

113 is the sum of two consecutive squares: 7² + 8². [Schlesinger]

It is possible to form seven sums of primes with the prime value of 113 using the first 22 primes: 2+19+31+61 = 3+37+73 = 5+41+67 = 7+49+59 = 11+23+79 = 13+29+71 = 17+43+53 = 113. [Gallardo]

``Theorem:'' Any number is prime. ``Proof:'' by the alphabet code, the phrase ``any number'' is 113. [Gallardo]

113 is the smallest prime such that the sum of the squares of the digits (11) is prime and the product of the digits (3) is also prime. Note that the concatenation of the two prime values (11 and 3) gives the prime number 113. [Capelle]

Raising 113 to the seventh power yields 15312283² + 9262³.

Longitude 113 degrees West passes through Dolphin Island in Great Salt Lake, Utah. Think of it as a "prime meridian" for the world's saltiest sailors.

The greatest known prime number p for which there is no prime number between p and p + sqrt(p). [Capelle]

The smallest prime that yields another if the sum of digits of its consecutive digits is sandwiched between each of the corresponding consecutive digits (i.e., 113 becomes 12143). [Silva]

The smallest prime whose number of digits and sum of digits are twin primes. [Silva]

The smallest prime number which is the sum of three fourth powers of primes. It is 2^4 + 2^4 + 3^4. [Hartley]

Let ψ(n) be the nautral logarithm of the least common multiple of all the numbers less than or equal to n (so ψ(6) = log(60)). The maximum value of ψ(n)/n occurs at 113. [RS62] [Caldwell]

The smallest zeroless three-digit prime. [Silva]