Super-prime

Super-prime

The subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers begins:3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, … OEIS|id=A006450.That is, if "p"("i") denotes the "i"th prime number, the numbers in this sequence are those of the form "p"("p"("i")); they have also been called super-prime numbers. harvtxt|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.

One can also define "higher-order" primeness much the same way, and obtain analogous sequences of primes. harvtxt|Fernandez|1999

A variation on this theme is the sequence of prime numbers with palindromic indices, beginning with :3, 5, 11, 17, 31, 547, 739, 877, 1087, 1153, 2081, 2381, … OEIS|id=A124173.

References

*citation
first1 = Robert E. | last1 = Dressler
first2 = S. Thomas | last2 = Parker
title = Primes with a prime subscript
journal = Journal of the ACM
volume = 22
issue = 3
year = 1975
pages = 380–381
id= MR|0376599
doi = 10.1145/321892.321900.
*citation
first1 =Neil | last1 = Fernandez
title = An order of primeness, F(p)
url = http://borve.org/primeness/FOP.html
year = 1999.

External links

* [http://acm.sgu.ru/problem.php?contest=0&problem=116 A Russian programming contest problem related to the work of Dressler and Parker]


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