In mathematics, a quartan prime is a prime number of the form x4 + y4, where x > 0, y > 0. The odd quartan primes are of the form 16n + 1.
For example, 17 is the smallest odd quartan prime: 17 = 14 + 24.
The first few quartan primes are
- 2, 17, 97, 257, 337, 641, 881, … (sequence A002645 in OEIS).
See also
References
- Neil Sloane, A Handbook of Integer Sequences, Academic Press, NY, 1973.
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| By formula |
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| By integer sequence |
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| By property |
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| Base-dependent |
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| Patterns |
- Twin (p, p + 2)
- Bi-twin chain (n − 1, n + 1, 2n − 1, 2n + 1, …)
- Triplet (p, p + 2 or p + 4, p + 6)
- Quadruplet (p, p + 2, p + 6, p + 8)
- k−Tuple
- Cousin (p, p + 4)
- Sexy (p, p + 6)
- Chen
- Sophie Germain (p, 2p + 1)
- Cunningham chain (p, 2p ± 1, …)
- Safe (p, (p − 1)/2)
- Arithmetic progression (p + a·n, n = 0, 1, …)
- Balanced (consecutive p − n, p, p + n)
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| By size |
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| Complex numbers |
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| Composite numbers |
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| Related topics |
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| First 100 primes |
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