# Sequence A080611: Lowest Base with Primality test for first N primes

This sequence, Sloane's A080611, gives the lowest base of a number system in which it is easy to test for the first N prime divisors.

For example, in base 10 it is easy to test for divisibility by 2 and 5 (by checking te last digit), by 3 (by casting out 9's), and by 11 (by alternately adding and subtracting the digits and noting if the answer is a multiple of 11, for example, to test 132: 1-3+2=0, therefore 132 is a multiple of 11.

So base 10 has tests for 2, 3, 5 and 11: the first three primes and one other. But in base 6, the same tests tell if a number is divisible by 2, 3, 5, and 7: the first 4 primes. Base 6 is the first base with tests for the first 4 primes, and thus 6 is the 4th term in the sequence.

The sequence runs: 2, 2, 4, 6, 21, 155, 441, 2925, 10165, 342056, 2781505, 10631544, 163886800, 498936010, 5163068911, 794010643700, 17635639237580, 353823355745574, 16828233620277430, 224220167903546529, 11990471619719586785, 113367767003198032480, 4446177962278202834685, 118332081735203144063619, 1103720538399012083835935, 78239926422758111576984420, ...

Another similar sequence is discussed here.

Some other sequences are discussed here.

mrob27
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