Truncatable primes
Problem 037: Truncatable primes
The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.
Find the sum of the only eleven primes that are both truncatable from left to right and right to left.
NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
Solution:
# ... #
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# ... #
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v < _^#`g03g00<
>"X"30g:10g%\10g/3+p30g>30g+:00g\` #v_$>30g1+:30p:10g%\10g/3+g" "-|
>90g"= ",,.@ ^p+3/g01\%g01:\" ":< ^ <
v < <
v ># ># $# v# -1<
$ >v >$\ v < >::.55+,90g+90pv
>:!#v_70p9> :70g55+*+:00g\`|>::10g%\10g/3+g"X"-#^_::55+\`#v_:55+/1\:!#^_55+/\55+*\v>::10g%\10g/3+g"X"-#v_\:50p%50g55+/\:|>| >\>:1-#^_$^
>$"= ",,90g.@ ^ < >$ #^!: #< >$$0 > ^> ^
^1$$<
Explanation:
The approach for this problem is to first iterate through the left-truncatable primes and test if these are right-truncatable. All with the help of our trusty companion the sieve of Eratosthenes.
Tricky was that the generation of left-truncatable primes, my original algorithm was recursive and I had to transform it to an iterative one for befunge.
| Interpreter steps: | 128 154 558 |
| Execution time (BefunExec): | 20s (6.19 MHz) |
| Program size: | 2000 x 514 |
| Solution: | 748317 |
| Solved at: | 2014-09-24 |