19937

Properties

Appears in sequences

• Mersenne exponents: primes p such that 2^p - 1 is prime. Then 2^p - 1 is called a Mersenne prime.at n=23A000043
• Degrees of primitive irreducible trinomials: n such that 2^n - 1 is a Mersenne prime and x^n + x^k + 1 is a primitive irreducible polynomial over GF(2) for some k with 0 < k < n.at n=15A001153
• Bertrand primes: a(n) is largest prime < 2*a(n-1) for n > 1, with a(1) = 2.at n=15A006992
• The smallest representative in a cycle of circular primes, where circular primes are numbers that remain prime under cyclic shifts of digits.at n=16A016114
• Numbers k such that the continued fraction for sqrt(k) has period 93.at n=17A020432
• Primes p such that p, p+12, p+24 are consecutive primes.at n=17A052188
• Primes p whose period of reciprocal equals (p-1)/7.at n=17A056212
• Numbers such that every cyclic permutation is a prime.at n=35A068652
• First of three consecutive Ulam numbers (A002858) in arithmetic progression with difference 22.at n=14A068856
• Primes of the form sum 6d/(2 + mu(d)) for some k and all d dividing k.at n=33A069548
• Prime(n) and prime(n+4) use the same digits.at n=18A069796
• Smallest prime p such that n applications of f lead form p to 2, where f is the mapping of primes > 2 to primes defined by A052248.at n=15A080190
• Numbers k such that Pi^k - 1/phi is closer to its nearest integer than any value of Pi^j - 1/phi for 1 <= j < k.at n=13A080281
• Balanced primes of order four.at n=21A082079
• Primes p of the form 2*prime(k) + 3 such that 2*prime(k+1) + 3 is the next prime after p.at n=39A089528
• Bisection of A000043.at n=11A099983
• Squares of the norms of Gaussian primes from A107629.at n=35A107630
• Primes p such that p's set of distinct digits is {1,3,7,9}.at n=16A108386
• One fifth of the sum of the first n primes, when an integer.at n=32A112271
• Mersenne prime indices that are not Gaussian primes.at n=13A112634