Concatenate two primes is also prime: Difference between revisions
Added Algol W
(Added Algol 68) |
(Added Algol W) |
||
Line 43:
print( ( newline, newline, "Found ", whole( c count, 0 ), " concat primes", newline ) )
END</lang>
{{out}}
<pre>
23 37 53 73 113 137 173 193 197 211
223 229 233 241 271 283 293 311 313 317
331 337 347 353 359 367 373 379 383 389
397 433 523 541 547 571 593 613 617 673
677 719 733 743 761 773 797 977 1117 1123
1129 1153 1171 1319 1361 1367 1373 1723 1741 1747
1753 1759 1783 1789 1913 1931 1973 1979 1997 2311
2341 2347 2371 2383 2389 2917 2953 2971 3119 3137
3167 3719 3761 3767 3779 3797 4111 4129 4153 4159
4337 4373 4397 4723 4729 4759 4783 4789 5323 5347
5923 5953 6113 6131 6143 6173 6197 6719 6737 6761
6779 7129 7159 7331 7919 7937 8311 8317 8329 8353
8389 8923 8929 8941 8971 9719 9743 9767
Found 128 concat primes
</pre>
=={{header|ALGOL W}}==
The Algol W for loop allows the loop counter values to be specified as a list - as there are only 25 primes below 100, this feature is used here to save looking through the sieve for the low primes.
<lang algolw>begin % find primes whose decimal representation is the concatenation of 2 primes %
integer MAX_PRIME;
MAX_PRIME := 99 * 99;
begin
logical array isPrime ( 1 :: MAX_PRIME );
logical array concatPrime ( 1 :: MAX_PRIME );
integer cCount;
% sieve the primes to MAX_PRIME %
isPrime( 1 ) := false; isPrime( 2 ) := true;
for i := 3 step 2 until MAX_PRIME do isPrime( i ) := true;
for i := 4 step 2 until MAX_PRIME do isPrime( i ) := false;
for i := 3 step 2 until truncate( sqrt( MAX_PRIME ) ) do begin
integer ii; ii := i + i;
if isPrime( i ) then for pr := i * i step ii until MAX_PRIME do isPrime( pr ) := false
end for_i ;
% find the concatenated primes, note their final digit can't be 2 or 5 %
for i := 1 until MAX_PRIME do concatPrime( i ) := false;
cCount := 0;
for p1 := 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 do begin
for p2 := 3, 7, 11, 13, 17, 19, 23, 29, 31, 37
, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 do begin
integer pc;
pc := ( p1 * ( if p2 < 10 then 10 else 100 ) ) + p2;
concatPrime( pc ) := isPrime( pc )
end for_p2
end for_p1;
% print the concatenated primes %
cCount := 0;
for i := 1 until MAX_PRIME do begin
if concatPrime( i ) then begin
writeon( i_w := 5, s_w := 0, i );
cCount := cCount + 1;
if cCount rem 10 = 0 then write()
end if_concatPrime_i
end for_i;
write();write( i_w := 1, s_w := 0, "Found ", cCount, " concat primes" )
end
end.</lang>
{{out}}
<pre>
| |||