# Ulam Primes

An Ulam number is a member of an integer sequence devised by and named after Stanislaw Ulam, who introduced it in 1964. The standard Ulam sequence (the (1, 2)-Ulam sequence) starts with U_{1} = 1 and U_{2} = 2. Then for n > 2, U_{n} is defined to be the smallest integer that is the sum of two distinct earlier terms in exactly one way and larger than all earlier terms.

As a consequence of the definition, 3 is an Ulam number (1+2); and 4 is an Ulam number (1+3). (Here 2+2 is not a second representation of 4, because the previous terms must be distinct.) The integer 5 is not an Ulam number, because 5 = 1 + 4 = 2 + 3.

A Ulam prime is a Ulam number that is also prime.

First 20: 2, 3, 11, 13, 47, 53, 97, 131, 197, 241, 409, 431, 607, 673, 739, 751, 983, 991, 1103, 1433

Checkout list of first: 10, 50, 100, 500, 1000 ulam primes. You can also check all ulam primes.

## Visualization#

Every frame counter is increased by one. If it is ulam prime then dot appears. Color has no meaning. Video has 25fps.

You can also compare it with other types.

## External#

- OEIS: A068820
- Wikipedia: Ulam prime
- Youtube: Visualization up to 1 million

## Tags#

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