But then, he says, it is absolutely necessary that the
basis of numeration should be a prime number. All other people think it
absolutely necessary that it should not, and regard the present basis as
only objectionable in not being divisible enough. But M. Comte's puerile
predilection for prime numbers almost passes belief. His reason is that
they are the type of irreductibility: each of them is a kind of ultimate
arithmetical fact. This, to any one who knows M. Comte in his later
aspects, is amply sufficient. Nothing can exceed his delight in anything
which says to the human mind, Thus far shalt thou go and no farther. If
prime numbers are precious, doubly prime numbers are doubly so; meaning
those which are not only themselves prime numbers, but the number which
marks their place in the series of prime numbers is a prime number.
Still greater is the dignity of trebly prime numbers; when the number
marking the place of this second number is also prime. The number
thirteen fulfils these conditions: it is a prime number, it is the
seventh prime number, and seven is the fifth prime number. Accordingly
he has an outrageous partiality to the number thirteen.
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