# Hazy Primes

Written by Paul Bourke
Inspired by Roy Blatchford, see original document
December 2017

A hazy prime of base "b" is a positive whole number that is not divisible (without remainder) by the first b prime numbers. The n'th hazy prime is denoted as Hb,n.

So for example the sequence of hazy primes H1,n are all the positive whole numbers not divisible by 2, namely the odd numbers.

The sequence H2,n are all the positive whole numbers not divisible by 2 and 3. The sequence up to 100 being 1 5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97.

The sequence up to 200 for H3,n is 1 7 11 13 17 19 23 29 31 37 41 43 47 49 53 59 61 67 71 73 77 79 83 89 91 97 101 103 107 109 113 119 121 127 131 133 137 139 143 149 151 157 161 163 167 169 173 179 181 187 191 193 197 199

The following table shows the base b on the vertical access and the hazy prime sequence on the horizontal axis. The base extends to 200 and the first 2000 items in the sequence shown. The red lines or spheres are primes.