## William Rowan Hamilton was born on this day 212 years ago.

## John Venn was born on this day 183 years ago.

### Properties of the number 3119:

3119 is a cyclic number.3119 and 3121 form a twin prime pair.

3119 has 21 antidivisors and 3118 totatives.

3119 has a semiprime digit sum 14 in base 10.

Reversing the decimal digits of 3119 results in a semiprime.

3119 = 1560

^{2}- 1559

^{2}is the difference of 2 nonnegative squares in 1 way.

3119 is the difference of 2 positive pentagonal numbers in 1 way.

3119 is not the sum of 3 positive squares.

3119

^{2}is the sum of 3 positive squares.

3119 is a proper divisor of 2

^{1559}- 1.

3119 = '31' + '19' is the concatenation of 2 prime numbers.

3119 is an emirp in (at least) the following bases: 2, 5, 15, 17, 19, 20, 24, 25, 27, 39, 42, 44, 46, 47, 51, 56, 58, 59, 68, 71, 72, 73, 76, 79, 81, 83, 85, 87, 88, 91, 92, 95, 97, and 100.

3119 is palindromic in (at least) the following bases: -15, and -38.

3119 in base 5 = 44434 and consists of only the digits '3' and '4'.

3119 in base 55 = 11d and consists of only the digits '1' and 'd'.

### The number 3119 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A001126: Primes with 7 as smallest primitive root.

A001154: Describe the previous term! (method A - initial term is 9).

A024770: Right-truncatable primes: every prefix is prime.

A045709: Primes with first digit 3.

A059452: Safe primes (A005385) which are not Sophie Germain primes.

A060229: Smaller member of a twin prime pair whose mean is a multiple of A002110(3)=30.

A068652: Numbers such that every cyclic permutation is a prime.

A142463: a(n) = 2*n^2 + 2*n - 1.

A164288: Members of A164368 which are not Ramanujan primes.

A215419: Primes that remain prime when a single digit 3 is inserted between any two consecutive digits or as the leading or trailing digit.

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