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Topic: 1 as a prime number
Replies: 11   Last Post: Dec 9, 1997 11:13 AM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: 1 as a prime number
Posted: Dec 9, 1997 10:52 AM
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On Mon, 8 Dec 1997, Vladimir Drobot wrote:

> On Mon, 8 Dec 1997, John Conway wrote:

> > I answered this at some length a few days ago. The tradition
> > before this century (dating back to Euclid's Elements) was indeed
> > to count 1 as a prime, and even Lehmer's 1914 list of prime numbers to
> > 10 million does so. But the many inconveniences it causes have
> > led people this century to put it into a new category, and call
> > it a "unit" rather than a prime.
> >
> > John Conway
> >

> Some of this presisted into this century. N. Lehmer (father of D. Lehmer)
> has published a count of primes up to some very large x, sometime in the
> early 20's. When people checked his results on a machine, they were off
> by one. It took a while to realize that he counted 1 as a prime.

I'm surprised to see you "correcting" my message like this. The
"count of primes up to some very large x" you are speaking about was
in fact the list of primes to 10 million that I mentioned above
(it actually goes a little bit further than that, so as to complete a
page), and its author was D.N.Lehmer, the father of D.H.Lehmer. Also,
as I correctly said, its publication date was 1914, not "some time in
the early 20's".

The story about "people checking his results on a machine" sounds
apocryphal to me. Lehmer's factor table and list of primes were the
standard works until about the 1960s, and everyone interested in
primes and factorization regularly consulted them. They were both
reprinted in the 1950's, and I obtained copies (which I still have)
in 1957. It's just possible, I suppose, that some ignoramus would
program his machine to count the primes below 10 million and be fooled
for a moment by the difference with Lehmer's count, but surely only for
a moment.

> In connection with this, there is a silly anecdote about late E.G.
> Strauss. People (non-mathematicians) would perpetually ask him for an
> opinion of why is 1 not a prime. One day he replied: Look, the primes are
> the buiding blocks of inetgers. But is is plain that 1 is not a brick.
> Sorry about that, I just could not resist.
> Vladimir Drobot

Apology accepted! John Conway

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