The Carmichael numbers up to \(10^{15}\). (English) Zbl 0780.11069
Summary: There are 105212 Carmichael numbers up to \(10^{15}\): we describe the calculations. The numbers were generated by a back-tracking search for possible prime factorizations, and the computations checked by searching selected ranges of integers directly using a sieving technique, together with a “large-prime variation”.
MSC:
| 11Y11 | Primality |
| 11A51 | Factorization; primality |
| 11-04 | Software, source code, etc. for problems pertaining to number theory |
Keywords:
Carmichael numbersOnline Encyclopedia of Integer Sequences:
a(n) = index of smallest Carmichael number (A002997) with n prime divisors, or 0 if no such number exists.a(n) = (k-1)/lambda(k), the index of the n-th Carmichael number k.
Number of four-prime Carmichael numbers less than 10^n.
Number of five-prime Carmichael numbers less than 10^n.
Number of six-prime Carmichael numbers less than 10^n.
Number of seven-prime Carmichael numbers less than 10^n.
Number of eight-prime Carmichael numbers less than 10^n.
Number of nine-prime Carmichael numbers less than 10^n.
Number of Carmichael numbers between 2^n and 2^(n+1).
Carmichael numbers congruent to 3 modulo 4.
Carmichael numbers that can be written as a product of two Carmichael numbers.
Weak Carmichael numbers.
Number of terms of A182116 between 2^n and 2^(n+1).
Let E(n,k) denote the k-th smallest Carmichael number such that there are n distinct Carmichael numbers: {x(1), x(2), ..., x(n)} where x_i < E_(n,k), such that for any integer i: 1 <= i <= n, x(i) is a quadratic residue of E(n,k).
