Carol primes (2n-1)2-2 and Kynea primes (2n+1)2-2

Current data

Base : 2 Max n : 768,870 Date : 2020-10-06

Carol: (44) 2, 3, 4, 6, 7, 10, 12, 15, 18, 19, 21, 25, 27, 55, 129, 132, 159, 171, 175, 315, 324, 358, 393, 435, 786, 1459, 1707, 2923, 6462, 14289, 39012, 51637, 100224, 108127, 110953, 175749, 185580, 226749, 248949, 253987, 520363, 653490, 688042, 695631 Kynea: (51) 1, 2, 3, 5, 8, 9, 12, 15, 17, 18, 21, 23, 27, 32, 51, 65, 87, 180, 242, 467, 491, 501, 507, 555, 591, 680, 800, 1070, 1650, 2813, 3281, 4217, 5153, 6287, 6365, 10088, 10367, 37035, 45873, 69312, 102435, 106380, 108888, 110615, 281621, 369581, 376050, 442052, 621443, 661478, 852770

History for both types

• 2020-10-06: Nothing, Dylan Delgado, released
• 2019-07-14: Found n = 852770, Ryan Propper
• 2018-12-13: Checked to n = 768870, Dylan Delgado
• 2018-11-12: Checked to n = 765831, Dylan Delgado
• 2018-05-02: Checked to n = 760000, Mark Rodenkirch
• 2016-09-19: Checked to n = 750000, Mark Rodenkirch
• 2016-08-27: Checked to n = 725000, Mark Rodenkirch
• 2016-07-22: Checked to n = 700000, Mark Rodenkirch
• 2016-07-17: Found n = 695631, Mark Rodenkirch
• 2016-07-06: Found n = 688042, Mark Rodenkirch
• 2016-06-26: Checked to n = 675000, Mark Rodenkirch
• 2016-06-18: Found n = 661478, Mark Rodenkirch
• 2016-06-14: Found n = 653490, Mark Rodenkirch
• 2016-06-12: Checked to n = 650000, Mark Rodenkirch
• 2016-05-31: Checked to n = 625000, Mark Rodenkirch
• 2016-05-30: Found n = 621443, Mark Rodenkirch
• 2016-05-21: Checked to n = 600000, Mark Rodenkirch
• 2016-04-27: Checked to n = 550000, Mark Rodenkirch
• 2016-04-15: Found n = 520363, Mark Rodenkirch
• 2016-04-07: Checked to n = 505000, Mark Rodenkirch
• 2016-03-25: Checked to n = 475000, Mark Rodenkirch
• 2016-02-29: Found n = 442052, Mark Rodenkirch, erroneous given as 442042
• 2016-02-06: Checked to n = 400000, Mark Rodenkirch
• 2016-02-10: Found n = 369581 & 376050, Mark Rodenkirch
• 2016-02-08: Checked to n = 360000, Mark Rodenkirch

History for Carol primes

• 2011-09-09: Checked n = 325000  -  350000, Albert J. Klein
• 2008-06-24: Checked n = 230001  -  250000, Japke Rosink
• 2007-05-03: Found n = 253987, Cletus Emmanuel
• 2006-04-04: Checked to n = 250000, Japke Rosink
• 2006-03-28: Found n = 248949, Japke Rosink
• 2005-08-04: Checked n = 210000  -  218000, Japke Rosink
• 2005-06-27: Checked n = 275000  -  325000, Japke Rosink
• 2005-04-25: Checked n = 218000  -  219000, Steven Harvey
• 2005-03-17: Checked n = 275000  -  291799, 297999  -  310768, 320000  -  325000, Japke Rosink
• 2005-02-13: Checked n = 219000  -  220000, Steven Harvey
• 2005-01-31: Checked n = 220000  -  230000, Steven Harvey
• 2005-01-11: Found n = 226749, Steven Harvey
• 2004-12-07: Checked to n = 200000, Cletus Emmanuel
• 2004-11-04: Checked to n = 187000, Cletus Emmanuel
• 2004-11-03: Found n = 185580, Cletus Emmanuel
• 2004-10-08: Checked n = 150000  -  175928, Cletus Emmanuel
• 2004-09-27: Checked n = 200000  -  210000, Rob Binnekamp
• 2004-04-22: Found n = 108127, Mark Rodenkirch; checked to n = 150000
• 2004-01-23: Found n = 110953, Rob Binnekamp
• 2004-01-19: Found n = 100224, Thomas Wolter
• 2002-07-03: Checked to n = 55000, Rob Binnekamp, Cletus Emmanuel
• 2002-03-10: Found n = 51637, Rob Binnekamp
• 2002: Found n = 39012, Steven Harvey
• 2002: Found n = 14289, Cletus Emmanuel; checked to n = 15000
• 2002-02-23: Found n = 14289, Cletus Emmanuel
• 2002-02-23: Found n = 6462, Cletus Emmanuel
• 2002-02-06: Found n = 1707 & 2923, Cletus Emmanuel

History for Kynea primes

• 2011-09-09: Checked n = 300000  -  342000, Albert J. Klein
• 2006-03-20: Checked to n = 300000, Cletus Emmanuel
• 2005-11-03: Checked to n = 285000, Cletus Emmanuel
• 2005-10-07: Found n = 281621, Cletus Emmanuel
• 2005-08-19: Checked n = 250000  -  275000, Cletus Emmanuel
• 2005-03-11: Checked to n = 250000, Predrag Minovic
• 2004-12-29: Checked to n = 243000, Predrag Minovic
• 2004-12-03: Checked to n = 240000, Predrag Minovic
• 2004-11-04: Checked to n = 233000, Predrag Minovic, Cletus Emmanuel
• 2004-09-08: Checked to n = 220000, Cletus Emmanuel
• 2004-06-28: Checked to n = 200000, Cletus Emmanuel
• 2004-04-16: Checked n = 150000  -  173000, Cletus Emmanuel
• 2004-04-07: Checked to n = 150000, Predrag Minovic
• 2004-03-26: Checked to n = 137000, Predrag Minovic
• 2004-03-10: Found n = 106380, Predrag Minovic
• 2004-02-18: Found n = 110615, Predrag Minovic
• 2004-02-24: Found n = 108888, Predrag Minovic
• 2004-02-23: Found n = 102435, Predrag Minovic
• 2002-07-03: Checked to n = 100000, Steven Harvey, Cletus Emmanuel
• 2002: Found n = 37035, 45873 & 69312, Steven Harvey
• 2002: Checked to n = 15000, Cletus Emmanuel
• 2002-02-23: Found n = 4217 - 10367, Cletus Emmanuel
• 2002-02-06: Found n = 2813 & 3281, Cletus Emmanuel

Explanations

• In the beginning of the search in 2002 by Cletus Emmanuel the Carol and Kynea primes were searched and sieved individually. Later in 2004 Multisieve supported both types.
• End of 2004 there was a bug reported in the sieve program, resieving has to be done then.
• Historical data from the project page by Steven Harvey, some dates from The Prime Pages and Yahoo Group "Primenumbers".