There's always more to discover about prime numbers and numbers that are not themselves prime but are associated with them. One such set of numbers is comprised of so-called interprimes. An interprime is defined by WolframAlpha as follows:
An interprime is the average of consecutive (but not necessarily twin) odd primes. The first few terms are 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, ... (OEIS A024675). The first few even interprimes are 4, 6, 12, 18, 26, 30, 34, 42, 50, 56, 60, ... (OEIS A072568), and the first few odd ones are 9, 15, 21, 39, 45, 69, 81, 93, 99, ... (OEIS A072569).
As well as the odd and even interprimes, there are other subsets as well including the one I discovered yesterday when investigating 24323. It turns out this numbers belongs to OEIS A075288: interprimes which are of the form s*prime, s=13 e.g. 1313 is an interprime and 1313/13 = 101 is prime. The sequence runs as follows:
26, 39, 1313, 4771, 7033, 9607, 11947, 12233, 14963, 15613, 18707, 20527, 24323
The OEIS lists sequences from s = 2 up to s = 21 (A075277-A075296). So yesterday I was halfway between two prime days (24317 and 24329). So I now have a new term and a new concept in my armoury. Of interest in this regard is the following (from WolframAlpha) - doubleclick to enlarge:
An interprime is the average of consecutive (but not necessarily twin) odd primes. The first few terms are 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, ... (OEIS A024675). The first few even interprimes are 4, 6, 12, 18, 26, 30, 34, 42, 50, 56, 60, ... (OEIS A072568), and the first few odd ones are 9, 15, 21, 39, 45, 69, 81, 93, 99, ... (OEIS A072569).
As well as the odd and even interprimes, there are other subsets as well including the one I discovered yesterday when investigating 24323. It turns out this numbers belongs to OEIS A075288: interprimes which are of the form s*prime, s=13 e.g. 1313 is an interprime and 1313/13 = 101 is prime. The sequence runs as follows:
26, 39, 1313, 4771, 7033, 9607, 11947, 12233, 14963, 15613, 18707, 20527, 24323
The OEIS lists sequences from s = 2 up to s = 21 (A075277-A075296). So yesterday I was halfway between two prime days (24317 and 24329). So I now have a new term and a new concept in my armoury. Of interest in this regard is the following (from WolframAlpha) - doubleclick to enlarge:
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