Prime Numbers - base patterns S.Ferguson

The Prime Numbers {2, 3, 5, 7, 11, ( base ten)} have different written formsdepending on the number base in which they are written. This has prompted manystudents to look for patterns for the primes in different bases, but alas! the primeswill not conform, and there is no one formula that will produce every Prime to be found, though - in particular, if we look at base six, we findthat the Prime Numbers from 5 upwards are of form 6n+1 or 6n-1; (but this doesn tmean that every number of form 6n 1 is Prime ).Here are the first 42 counting Numbers arranged in six columns; with the exceptionof 2 and 3 the primes, printed in bold italic, fall into columns one and five - to Numbers of the form 6n we rewrite our table, with the Numbers now written in base six instead of baseten, the pattern becomes much more obvious:12345101112131415202122232425303 1323334354041424344455051525354551001011 02103104105110

BASE TWELVE AND THE PRIME NUMBERS (by Don Hammond, in Dozenal Journal no. 5) The dozenal base quickly and easily reveals a fundamental property of prime numbers. For natural numbers in base twelve greater than 3:

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  Base, Number, Prime, Fundamentals, Patterns, Prime numbers base patterns

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