167 (number)

167 prime 39th, chen, gaussian, safe 1, 167 167 (one hundred [and] sixty-seven) is the natural number following 166 and preceding 168. In mathematics 167 is the 39th prime number, an emirp, an isolated prime, a Chen prime,A109611 Chen primes: primes p such that p + 2 is either a prime or a semiprime a Gaussian prime, a safe prime,A005385 Safe primes and an Eisenstein prime with no imaginary part and a real part of the form . 167 is the smallest number which requires six terms when expressed using the greedy algorithm as a sum of squares, 167 = 144 + 16 + 4 + 1 + 1 + 1,A006892 Representation as a sum of squares requires n squares with greedy algorithm although by Lagrange's four-square theorem its non-greedy expression as a sum of squares can be shorter, e.g. 167 = 121 + 36 + 9 + 1. 167 is a full reptend prime in base 10, since the decimal expansion of 1/167 repeats the following 166 digits: 0.00598802395209580838323353293413173652694610778443113772455089820359281437125748502994 0119760479041916167664670658682634730538922155688622754491017964071856287425149700... 167 is a highly cototient number, as it is the smallest number k with exactly 15 solutions to the equation x - φ(x) = k. It is also a strictly non-palindromic number. 167 is the smallest multi-digit prime such that the product of digits is equal to the number of digits times the sum of the digits, i. e., 1×6×7 = 3×(1+6+7) 167 is the smallest positive integer d such that the imaginary quadratic field Q(–d) has class number = 11.Tables of imaginary quadratic fields with small class number numbertheory.org http://www.numbertheory.org/classnos/ References External links Prime curiosities: 167 1 Category:Integers Category: Prime numbers