Members of the imaginary quadratic field Q(sqrt(-1)) and form a ring often denoted Z[i], or sometimes k(i) that are prime. (primes of the form 4n + 3) 3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107, 127, 131, 139, 151, 163, 167, 179, 191, 199, 211, 223, 227, 239, 251, 263, 271, 283, 307, 311, 331, 347, 359, 367, 379, 383, 419, 431, 439, 443, 463, 467, 479, 487, 491, 499, 503
Odd primes p which divide the class number of the p-th cyclotomic field. 37, 59, 67, 101, 103, 131, 149, 157, 233, 257, 263, 271, 283, 293, 307, 311, 347, 353, 379, 389, 401, 409, 421, 433, 461, 463, 467, 491, 523, 541, 547, 557, 577, 587, 593, 607, 613, 617, 619
Let d(p) be the shadow of the sequence f(n) = seq1-1(n) (which gives the number of sequences without repetitions that can be obtained from n distinct objects), i.e. the count of sequence entries f(0), f(1), f(2), ...., f(h-1) divisible by an integer h. If d(p) = 0, then p is this type of prime. 3, 7, 11, 17, 47, 53, 61, 67, 73, 79, 89, 101, 139, 151, 157, 191, 199
Primes p for which the least positive primitive root is not a primitive root of p2. 2, 40487, 6692367337
Primes p for which the binomial coefficient (2p - 1)! / [ (p - 1)! ((2p - 1) - (p - 1))! ] ≡ 1 (mod p4). 16843, 2124679 As of 2011, these are the only known Wolstenholme primes.
Of the form pn# −1 or pn# + 1. 3, 5, 7, 29, 31, 211, 2309, 2311, 30029, 200560490131, 304250263527209, 23768741896345550770650537601358309
Primes p for which there are no solutions to Hk ≡ 0 (mod p) and Hk ≡ −ωp (mod p) for 1 ≤ k ≤ p−2, where ωp is the Wolstenholme quotient. 5, 13, 17, 23, 41, 67, 73, 79, 107, 113, 139, 149, 157, 179, 191, 193, 223, 239, 241, 251, 263, 277, 281, 293, 307, 311, 317, 331, 337, 349
A prime number p which has more solutions to the equation x − φ(x) = p, than any other integer below p and above one, where, φ is Euler's totient function. 2, 23, 47, 59, 83, 89, 113, 167, 269, 389, 419, 509, 659, 839, 1049, 1259, 1889
Of the form pn# + 1 (a subset of primorial primes), where pn# is the nth primorial, i.e. the product of the first n primes. 3, 7, 31, 211, 2311, 200560490131
Primes that are the number of partitions of a set with n members. 2, 5, 877, 27644437, 35742549198872617291353508656626642567, 359334085968622831041960188598043661065388726959079837 The next term has 6,539 digits.
Of the form ⌊θ3n⌋, where θ is an eponymous constant. Its value is unknown, but if the Riemann hypothesis is true it is approximately 1.3063778838630806904686144926... This form is prime for all positive integers n. 2, 11, 1361, 2521008887, 16022236204009818131831320183
A prime number from an eponymous number sequence that can be used to count certain kinds of binary trees. The first few numbers are: 0, 1, 1, 1, 2, 3, 6, 11, 23, 46, 98, 207, 451, 983, 2179, 4850, 10905, 24631, 56011, ... 2, 3, 11, 23, 983, 2179, 24631, 3626149, 253450711, 596572387
Primes p such that (p, p−5) is an irregular pair. 37 Primes p such that (p, p−9) is an irregular pair. 67, 877
Those numbers which are prime AND for which the following process ends in 1: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. 7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383, 397, 409, 487, 563, 617, 653, 673, 683, 709, 739, 761, 863, 881, 907, 937, 1009, 1033, 1039, 1093
Primes pn for which pn2 > pn−i pn+i for all 1 ≤ i ≤ n−1, where pn is the nth prime. 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179, 191, 223, 227, 251, 257, 269, 307
A number that remains prime on any cyclic rotation of its digits (in base 10). 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 197, 199, 311, 337, 373, 719, 733, 919, 971, 991, 1193, 1931, 3119, 3779, 7793, 7937, 9311, 9377, 11939, 19391, 19937, 37199, 39119, 71993, 91193, 93719, 93911, 99371, 193939, 199933, 319993, 331999, 391939, 393919, 919393, 933199, 939193, 939391, 993319, 999331 Some sources (including OEIS) only list the smallest prime in each cycle, for example listing 13 but omitting 31.
A member of the sequence Gn that satisfies the relation: 2t / ( et + 1 ) = SUMMATION [from n=1 it infinity] [ Gn ( tn / n! )] that is also prime. 17 is conjectured to be the only such prime.
A prime divisor of the order of the Monster group M, the largest of the sporadic simple groups. There are precisely 15 such primes: all 15 are Chen primes. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71
Primes of the form n ʅ ± 1, where n ʅ denotes the swinging factorial, which is defined in terms of the double swinging factorial as n ʅ = (n-1) ʅ ʅ n ʅ ʅ and n ʅ ʅ = 1 for n ≤ 0 and n ʅ ʅ = (n - 2) ʅ ʅ n[ n odd ] ( 4 / n )[ n even ] for n > 0. 2, 3, 5, 7, 19, 29, 31, 71, 139, 251, 631, 3433, 12011
Of the form 2u3v + 1 for some integers u,v ≥ 0. These are also class 1- primes. 2, 3, 5, 7, 13, 17, 19, 37, 73, 97, 109, 163, 193, 257, 433, 487, 577, 769, 1153, 1297, 1459, 2593, 2917, 3457, 3889, 10369, 12289, 17497, 18433, 39367, 52489, 65537, 139969, 147457
The list of primes p for which the period length of the decimal expansion of 1/p is unique (no other prime gives the same period). 3, 11, 37, 101, 9091, 9901, 333667, 909091, 99990001, 999999000001, 9999999900000001, 909090909090909091, 1111111111111111111, 11111111111111111111111, 900900900900990990990991
A prime number, n, such that when a Fibonacci sequence is formed with the first term equal to the absolute value of the successive differences between consecutive digits of n and the second term equal to the sum of the decimal digits of n, n itself appears as a term in this Fibonacci sequence. 29, 683, 997, 2207, 30571351
Primes p for which, ( bp-1 - 1) / p in a given base b, gives a cyclic number. Primes p for base 10: 7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, 167, 179, 181, 193, 223, 229, 233, 257, 263, 269, 313, 337, 367, 379, 383, 389, 419, 433, 461, 487, 491, 499, 503, 509, 541, 571, 577, 593
Primes p which do not divide the class number of the p-th cyclotomic field. 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53, 61, 71, 73, 79, 83, 89, 97, 107, 109, 113, 127, 137, 139, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 239, 241, 251, 269, 277, 281
A prime p > 5 if p2 divides the Fibonacci number Fp - (p/5), where the Legendre symbol (p/5) is defined as (p/5) = 1 for p ≡ ± 1 (mod 5) and (p/5) = - 1 for p ≡ ± 2 (mod 5). As of 2013, no Wall-Sun-Sun primes are known.
Primes with a prime index in the sequence of prime numbers (the 2nd, 3rd, 5th, ... prime). 3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353, 367, 401, 431, 461, 509, 547, 563, 587, 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991
Quiz Playlist
Details
More Info:
(Stupidly Insane): Emphasis on STUPIDLY!!! This is third of a 4 part series. Each gets successively more difficult.
Clickable: Select answers by clicking on text or image buttons
In order to create a playlist on Sporcle, you need to verify the email address you used during registration. Go to your Sporcle Settings to finish the process.
Comments