Concatenate two primes is also prime: Difference between revisions
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m (→{{header|REXX}}: expanded output title, added/changed comments and whitespace.) |
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=={{header|REXX}}== |
=={{header|REXX}}== |
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<lang rexx>/*REXX pgm finds |
<lang rexx>/*REXX pgm finds base ten neighbor primes P1 & P2, when concatenated, is also a prime.*/ |
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parse arg hip cols . /*obtain optional arguments from the CL*/ |
parse arg hip cols . /*obtain optional arguments from the CL*/ |
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if hip=='' | hip=="," then hip= 100 /*Not specified? Then use the default.*/ |
if hip=='' | hip=="," then hip= 100 /*Not specified? Then use the default.*/ |
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if cols=='' | cols=="," then cols= 10 /* " " " " " " */ |
if cols=='' | cols=="," then cols= 10 /* " " " " " " */ |
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call genP /*build array of semaphores for primes.*/ |
call genP /*build array of semaphores for primes.*/ |
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title= ' concatenation of two primes (P1, P2) in base ten that results in |
title= ' concatenation of two neighbor primes (P1, P2) in base ten that results in' , |
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"a prime, where P1 & P2 are <" commas(hip) |
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w= 10 /*width of a number in any column. */ |
w= 10 /*width of a number in any column. */ |
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if cols>0 then say ' index │'center(title, 1 + cols*(w+1) ) |
if cols>0 then say ' index │'center(title, 1 + cols*(w+1) ) |
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do j=1 for ## /*search through specified primes. */ |
do j=1 for ## /*search through specified primes. */ |
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do k=1 for ##; cat2= @.j || @.k /*create a concatenated prime (base 10)*/ |
do k=1 for ##; cat2= @.j || @.k /*create a concatenated prime (base 10)*/ |
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if !.cat2 then a.cat2= 1 /*flag it as being a "2cat" prime. */ |
if !.cat2 then a.cat2= 1 /*flag it as being a "2cat" prime. */ |
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end /*k*/ /* [↑] forgoes the need for sorting. */ |
end /*k*/ /* [↑] forgoes the need for sorting. */ |
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end /*j*/ |
end /*j*/ |
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found= 0; |
found= 0; idx= 1 /*initialize # of primes found; IDX. */ |
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$=; do n=1 by 2 for hip**2%2 /*search for odd "cat2" primes. */ |
$=; do n=1 by 2 for hip**2%2 /*search for odd "cat2" primes. */ |
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if \a.n then iterate /*search through allowable primes. */ |
if \a.n then iterate /*search through allowable primes. */ |
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if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─') |
if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─') |
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say |
say |
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say 'Found ' |
say 'Found ' commas(found) title |
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exit 0 /*stick a fork in it, we're all done. */ |
exit 0 /*stick a fork in it, we're all done. */ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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#= 5; sq.#= @.#**2 /*the square of the highest low prime. */ |
#= 5; sq.#= @.#**2 /*the square of the highest low prime. */ |
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do j=@.#+2 by 2 to hip**2-1 /*find odd primes from here on. */ |
do j=@.#+2 by 2 to hip**2-1 /*find odd primes from here on. */ |
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parse var j '' -1 _; |
parse var j '' -1 _; if _==5 then iterate /*J ÷ by 5? (right digit).*/ |
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if j//3==0 then iterate; if j//7==0 then iterate /*" " " 3? J ÷ by 7? */ |
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if j// 7==0 then iterate /*" " " 7? */ |
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do k=5 while sq.k<=j /* [↓] divide by the known odd primes.*/ |
do k=5 while sq.k<=j /* [↓] divide by the known odd primes.*/ |
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if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */ |
if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */ |
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{{out|output|text= when using the default inputs:}} |
{{out|output|text= when using the default inputs:}} |
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<pre> |
<pre> |
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index │ |
index │ concatenation of two neighbor primes (P1, P2) in base ten that results in a prime, where P1 & P2 are < 100 |
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───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── |
───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── |
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1 │ 23 37 53 73 113 137 173 193 197 211 |
1 │ 23 37 53 73 113 137 173 193 197 211 |
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───────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────── |
───────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────── |
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Found 128 concatenation of two primes (P1, P2) in base ten that results in a prime, |
Found 128 concatenation of two neighbor primes (P1, P2) in base ten that results in a prime, where P1 & P2 are < 100 |
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</pre> |
</pre> |
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