A fifth entry in our "Numeric T-Shirt" line:
Back of T-Shirt: "The smallest 3-digit emirp!"
Front: __ __ __ ?
A "emirp" is a prime number which forms a different prime number when its digits are reversed. (Palindromic primes are excluded by this definition.)
Not much new work here - we borrowed the IsPrime and Reverse functions from T-Shirt #4 . So all that is left for the SearchBtnClick method is to run through a loop looking for primes, checking if the reverse is a prime, and checking that they are not the same. If a number that meets these three conditions, add it to a display list.
I added a TUpDown box to select how many digits, N, in the emirps of interest. A 3-line IntPower function lets us set the lower limit of our search as 10(N-1) and the upper limit at one less than 10 times the lower limit. For 3-digit emirps for example, that means that at most we'll search from 10(3-1) = 102 = 100 up to 10×100-1=1000-1=999. That pretty much covers the 3-digit candidates. We search for emirps up to 9 digits, so we'll limit the display to 100 hits - we really don't need thousands (or millions) of them displayed.
About 50 lines of code here, well within the beginner's range.
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This program
let's us search for emirps from 2 to 9 digits. The largest value for 32
bit integer types is a little over 2 billion so numbers up to
999,999,999 can be tested. Of course int64 type, 64 bit
integers, could test up to somewhere around 1019 if you
would prefer the smallest 19-digit emirp on your shirt. By
the way, n binary digits (bits) can represent decimal numbers up to
about 0.3n digits. Why? Here's a hint, thanks to the miracle of
logarithms:
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This is just one of those "reasonableness" checks that can be handy when making quick estimates.
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Why aren't there there any one digit emirps? |
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What if we wanted the largest n-digit emirp? |
| Originally posted: July 27, 2002 | Modified:November 07, 2008 |