# 311

This number is a prime.  Band 311 (pronounced "three eleven") got their name from a police code after one of the band's former members was charged with indecent exposure. [Puckett] The Federal Communications Commission (FCC) set aside the prime number 311, a telephone code now used in many U.S. Cities, for connection to police non-emergencies. 311 is the eleventh three-digit prime for which the sum of the squares of its digits is also a prime. Note that the sum here is eleven as well. [Trotter] 311 is the smallest number expressible as the sum of consecutive primes in four ways. [De Geest] Apartment number 311 is the first door to be knocked on in the movie Ace Ventura: Pet Detective. [Shadyac] Mickey Mantle's rookie card number 311 is prime. Note also that M+I+C+K+E+Y+M+A+N+T+L+E = 131 (A=1...Z=26), another prime which happens to contain the same digits as his rookie card number. [Rupinski] A right-truncatable prime that can be obtained by concatenating the first three non-composite digits of π. [Necula] The smallest three-digit prime that is the sum of three different three-digit primes. [Gallardo] Lesser of the first occurrence of a twin prime (311, 313) such that sets of digits of both primes are equal. [Firoozbakht] Timothy Leary claimed to have taken LSD a total of 311 times. [Coeburn] The largest prime of the form |a^b - c^d|, where a, b, c and d are the first 4 primes. 311 = 7^3 - 2^5. Curiously, 311 = prime(2^6). [Post] The smallest home prime for composite numbers, that is an emirp. [Loungrides] 311 trillion years is the span of a wide era called mahamantavara on the Vedic Hindu time scale. [Beedassy] Sources of narrow spectrum radiation (UVB 311 nm) are considered to be the best for vitiligo and psoriasis treatment. [Homewood] Describing this emirp (one 3, two 1) yields another (1321). [Silva] The only prime (emirp) that can be represented as p p’s minus q q’s, where p, q are successive primes, i.e., 333-22. [Loungrides] The Transportation Security Administration (TSA) has a "3-1-1" for carry-ons. The smallest prime (emirp) that is the first of six consecutive primes that remain prime if you delete their first digit, i.e., 311, 313, 317, 331, 337, 347. [Loungrides] "The End and the Beginning" begins on page 311 of Paulo's book Prime Numbers, Friends Who Give Problems. The smallest prime p such that every integer from 2 to 10 is a quadratic residue mod p. [Ewing] There are 3^11 different ways to tie the knot of a necktie. [Vejdemo-Johansson] The smallest prime number that is an anagram of two smaller primes. [Gaydos] The smallest emirp that can be represented as sum of the four powers a^a+b^b+c^c+d^d where abcd is a 4-digit prime p, i.e., (p=1433), with 1^1+4^4+3^3+3^3=311. [Loungrides]

(There are 9 curios for this number that have not yet been approved by an editor.)