A Kynéa number (pronounced: Ka-Nay), named after Kynéa R. Griffith, is an integer of the form 4ⁿ + 2^{n + 1} − 1. An equivalent formula is (2ⁿ + 1)² − 2. This indicates that a Kynéa number is the nth power of 4 plus the (n + 1)th Mersenne number. The first few Kynéa numbers are In mathematics, a Mersenne prime is a prime number that is one less than a power of two. ...

7, 23, 79, 287, 1087, 4223, 16639, 66047, 263167, 1050623, 4198399, 16785407 (sequence A093069 in OEIS) This article is about the number seven. ... 23 (twenty-three) is the natural number following 22 and preceding 24. ... 79 is the natural number following 78 and preceding 80. ... The On-Line Encyclopedia of Integer Sequences (OEIS) is a web-based searchable database of integer sequences. ...

The binary representation of the nth Kynéa number is a single leading one, followed by n - 1 consecutive zeroes, followed by n + 1 consecutive ones.

So, for example, 23 is 10111 in binary, 79 is 1001111, etc. The difference between the nth Kynéa number and the nth Carol number is the (n + 2)th power of two. We dont have an article called Carol number Start this article Search for Carol number in. ... In mathematics, a power of two is any of the nonnegative integer powers of the number two; in other words, two times itself a certain number of times. ...

Starting with 7, every third Kynéa number is a multiple of 7. Thus, for a Kynéa number to also be a prime number, its index n can not be of the form 3x + 1 for x > 0. The first few Kynéa numbers that are also prime are 7, 23, 79, 1087, 66047, 263167, 16785407 (these are listed in Sloane's A091514). As of 2006, the largest known Kynéa number that is also a prime is the Kynéa number for n = 281621, approximately 5.455289117190661 × 10¹⁶⁹⁵⁵². It was found by Cletus Emmanuel in November of 2005, using k-Sieve from Phil Comody and OpenPFGW. This is the 46th Kynéa prime. These numbers were first encountered in 1994 by Cletus Emmanuel. In mathematics, a prime number (or prime) is a natural number greater than one whose only positive divisors are one and itself. ...

External link

• Prime Database entry for Kynea(281621)