| Kynea Number |
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7 , 23 , 79 , 287, 1087, 4223, 16639, 66047, 263167, 1050623, 4198399, 16785407 The binary representation of the ''n''th 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 ''n''th Kynéa number and the ''n''th Carol Number is the (''n'' + 2)th Power Of Two . 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 3''x'' + 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 ). 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. EXTERNAL LINK |
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