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Carol number
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(Definition)
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Given  , compute
 or
 or
 or
Any of these formulas gives the Carol number for  . Regardless of how they're computed, these numbers are almost repunits in binary, needing only the addition of  to become so.
The first few Carol numbers are 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527, 4190207, 16769023 (listed in A093112 of Sloane's OEIS). Every third Carol number is divisible by 7, thus prime Carol numbers can't have
 (except of course for  . The largest Carol number known to be prime is
 , found by Japke Rosink using MultiSieve and OpenPFGW in March 2006.
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"Carol number" is owned by Mravinci.
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(view preamble | get metadata)
Cross-references: OpenPFGW, multisieve, prime, divisible, OEIS, addition, binary, repunits, numbers
This is version 2 of Carol number, born on 2006-09-06, modified 2006-09-07.
Object id is 8317, canonical name is CarolNumber.
Accessed 713 times total.
Classification:
| AMS MSC: | 11N05 (Number theory :: Multiplicative number theory :: Distribution of primes) |
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Pending Errata and Addenda
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