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 U1 = 1 and U2 = 2. Then for n > 2, Un 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
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