Prime Kynea Numbers
Starting with 7, every third Kynea number is a multiple of 7. Thus, for a Kynea number to be a prime number, its index n can not be of the form 3x + 1 for x > 0. The first few Kynea numbers that are also prime are 7, 23, 79, 1087, 66047, 263167, 16785407 (sequence A091514 in OEIS).
As of 2006, the largest known prime Kynea number has index n = 281621 and approximately equals 5.5×10169552. It was found by Cletus Emmanuel in November 2005, using k-Sieve from Phil Carmody and OpenPFGW. This is the 46th Kynea prime.
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