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Base-dependent classifications of prime numbers
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Classifications of primes depending on their base representation.
(see also: base-independent classifications of prime numbers)
Table of base dependent classifications of prime numbers
Note that under the banner of reversible primes fall both the emirps and the palindromic primes (which in turn also includes the repunit primes).
For the sake of brevity, and to avoid redundancy, 1-digit primes (in the base at hand) have been omitted from this table. And for the sake of convenience, these are all written here in base 10 (which is the usual procedure throughout the OEIS).
Binary (Base 2) |
Quinary (Base 5) |
Octal (Base 8) |
Decimal (Base 10) |
Duodecimal (Base 12) |
Hexadecimal (Base 16) |
Vigesimal (Base 20) |
Sexatrigesimal (Base 36) | |
---|---|---|---|---|---|---|---|---|
Absolute primes | A000668 (trivially)^{[1]} | {11, 13, 17, 19, 23, 31, ...} | {13, 29, 31, 41, 43, 47, 59, 61, 73, ...} | A003459 | {13, 17, 61, 67, 71, 89, 137, 157, 163, 167, 229, 277, ...} | {17, 23, 31, 53, 59, 61, 83, 89, ...} | {23, 29, 61, 71, 73, 79, ...} | {37, 41, 47, 53, 59, 67, 181, 191, 197, ...} |
Emirps | A080790 | {7, 11, 13, 17, 19, 23, 29, 37, 47, ...} | {13, 29, 31, 41, 43, 47, 59, 61, 67, 71, 79, ...} | A006567 | {17, 61, 67, 71, 89, 137, 151, 163, ...} | {23, 31, 53, 59, 61, 83, 89, ...} | {23, 29, 61, 71, 73, 79, ...} | {41, 47, 53, 59, 67, ...} |
Palindromic primes | A016041 | A029973 | A029976 | A002385 | A029979 | A029732 | {401, 421, 461, ...} | {37, 1297, 1549, 1621, 1657, 1693, ...} |
Pandigital primes | A138837^{[2]} | A175277 | A175271 | A050288 | A175272 | A175273 | A175274 | Numbers too large to fit in this cell^{[3]} |
Repunit primes | A000668 | {31, 19531, ...} | {73, ...} | Indexed by A004023 | {13, 157, 22621, ...} | {17, ... | {421, 10778947368421, ...} | {37, ...} |
Reversible primes | A074832 | A075235 | A075238 | A007500 | {13, 17, 61, 67, 71, 89, 137, ...} | {17, 23, 31, 53, 59, 61, 83, 89, ...} | {23, 29, 61, 71, 73, 79, ...} | {23, 29, 31, 37, 41, 47, 53, 59, 67, 181, ...} |
Smarandache-Wellin primes | {2, 11, 751, ...} | {2, 13, ...} | {2, 19, 157, ...} | A069151 | {2, 6835837, ...} | {2, 144763, ...} | {2, 43, P78,^{[4]} ...} | {2, 97387, ...} |
See also
Notes
- ↑ Since these consist of all 1s, any digit permutation results in the same number.
- ↑ This works out to be the non-Mersenne primes since only two distinct digits are necessary and only the Mersenne primes lack significant zeroes.
- ↑ The first six are 106474205747327721970821813283682888755465951838540182351, 106474205747327721970821813283682888755465951838655934631, 106474205747327721970821813283682888755465951838716447391, 106474205747327721970821813283682888755465951838776957771, 106474205747327721970821813283682888755465951838718031211, 106474205747327721970821813283682888755465951838781855251.
- ↑ P78 = 124714291526815004837197861656712864978058848205357894140728554591060949014939.