Super Primes
Super-prime numbers (also known as higher-order primes or prime-indexed primes) are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
That is, if p(i) denotes the ith prime number, the numbers in this sequence are those of the form p(p(i)). Dressler & Parker (1975) used a computer-aided proof (based on calculations involving the subset sum problem) to show that every integer greater than 96 may be represented as a sum of distinct super-prime numbers. Their proof relies on a result resembling Bertrand's postulate, stating that (after the larger gap between super-primes 5 and 11) each super-prime number is less than twice its predecessor in the sequence.
First 20: 3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353
Checkout list of first: 10, 50, 100, 500, 1000 super primes. You can also check all super primes.
Visualization#
Every frame counter is increased by one. If it is super prime then dot appears. Color has no meaning. Video has 25fps.
You can also compare it with other types.
External#
- OEIS: A006450
- Wikipedia: Super-prime
- Youtube: Visualization up to 1 million
Tags#
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