A minor number theory note.

Based on some back of the envelope estimates, there should be only a finite number of rotational primes in base 10. (I haven't double-checked my estimates closely, but I find it suggestive that you have 4 of size 1, and none of size 7.)

However my estimates suggesting this were based on the standard, "Treat is_prime(n) as a random number with probability 1/log(n) of being true." This is a simple rule of thumb which leads to a lot of estimates in number theory, most of which are strongly supported by the numerical evidence. (For instance the prime number theorem is true, the Riemann Hypothesis should be, the twin prime conjecture should be, Mertens Conjecture should be false but the numerical evidence will make it look true for an absurdly long time, etc.)

Unfortunately it is a rule of thumb that is absolutely and horribly wrong, with the result that number theory is full of gloriously precise conjectures on primes which have very strong affirmative evidence, but which are not readily amenable to proof.

UPDATE: As I point out at Re^2: Rotationally Prime Numbers Revisited, I think this post is wrong. (I forgot about numbers that are just strings of 1s.)

In reply to Re (tilly) 1: Rotationally Prime Numbers by tilly
in thread Rotationally Prime Numbers by YuckFoo

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.