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Truncatable primes
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| using Primes | |
| function appendLeft(num, base, prims = []) | |
| for n in 1:(base-1) | |
| leftAppended = parse(BigInt, "$n$num", base = base) | |
| if isprime(leftAppended) | |
| appendLeft("$n$num", base, prims) | |
| else | |
| if ("$num" in prims) == false | |
| push!(prims, "$num") | |
| end | |
| end | |
| end | |
| return prims | |
| end | |
| function appendRight(num, base, prims = []) | |
| for n in 0:(base-1) | |
| rightAppended = parse(BigInt, "$num$n", base = base) | |
| if isprime(rightAppended) | |
| appendRight("$num$n", base, prims) | |
| else | |
| if ("$num" in prims) == false | |
| push!(prims, "$num") | |
| end | |
| end | |
| end | |
| return prims | |
| end | |
| for base in 3:10 | |
| lhp = Dict() | |
| rhp = Dict() | |
| for i in primes(base - 1) | |
| if (base in keys(lhp)) == false | |
| lhp[base] = Dict() | |
| end | |
| if (base in keys(rhp)) == false | |
| rhp[base] = Dict() | |
| end | |
| lhp[base][i] = appendLeft(i, base) | |
| rhp[base][i] = appendRight(i, base) | |
| end | |
| lhprimes = sort(map(x -> typeof(x) == String ? parse(BigInt, x) : x, collect(Iterators.flatten(values(lhp[base]))))) | |
| rhprimes = sort(map(x -> typeof(x) == String ? parse(BigInt, x) : x, collect(Iterators.flatten(values(rhp[base]))))) | |
| bsprimes = intersect(lhprimes, rhprimes) | |
| println("\nBase $base") | |
| println("Largest left-truncating prime: $(lhprimes[length(lhprimes)]) ($(length(lhprimes)))") | |
| println("Largest right-truncating prime: $(rhprimes[length(rhprimes)]) ($(length(rhprimes)))") | |
| println("Largest both-sides truncating prime: $(bsprimes[length(bsprimes)]) ($(length(bsprimes)))") | |
| end | |
| #= | |
| +------+-------+--------------------------+-------+-------------+--------+--------------+ | |
| | Base | # LTP | Largest LTP | # RTP | Largest RTP | # both | Largest both | | |
| +------+-------+--------------------------+-------+-------------+--------+--------------+ | |
| | 3 | 3 | 212 | 4 | 2122 | 2 | 212 | | |
| +------+-------+--------------------------+-------+-------------+--------+--------------+ | |
| | 4 | 16 | 333323 | 7 | 2333 | 3 | 23 | | |
| +------+-------+--------------------------+-------+-------------+--------+--------------+ | |
| | 5 | 15 | 222232 | 14 | 34222 | 5 | 232 | | |
| +------+-------+--------------------------+-------+-------------+--------+--------------+ | |
| | 6 | 454 | 14141511414451435 | 36 | 2155555 | 9 | 3515 | | |
| +------+-------+--------------------------+-------+-------------+--------+--------------+ | |
| | 7 | 22 | 6642623 | 19 | 25642 | 7 | 52 | | |
| +------+-------+--------------------------+-------+-------------+--------+--------------+ | |
| | 8 | 446 | 3136361655377775 | 68 | 21117717 | 22 | 3513 | | |
| +------+-------+--------------------------+-------+-------------+--------+--------------+ | |
| | 9 | 108 | 4284484465 | 68 | 3444224222 | 8 | 212 | | |
| +------+-------+--------------------------+-------+-------------+--------+--------------+ | |
| | 10 | 4260 | 357686312646216567629137 | 83 | 73939133 | 15 | 739397 | | |
| +------+-------+--------------------------+-------+-------------+--------+--------------+ | |
| =# |
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