Prime numbers p for which the sum of primes less than or equal to p is prime: Difference between revisions
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(Added Algol 68 sample (same as the modified Sumarie primes sample)) |
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Find primes '''p''' which the sum of primes less or equal to '''p''' is prime, where '''p < 1,000'''. |
Find primes '''p''' which the sum of primes less or equal to '''p''' is prime, where '''p < 1,000'''. |
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<br><br> |
<br><br> |
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=={{header|ALGOL 68}}== |
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Same as the [[Summarize primes#ALGOL_68]] solution. |
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<lang algol68>BEGIN # sum the primes below n and report the sums that are prime # |
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INT max prime = 999; # largest prime to consider # |
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# sieve the primes to max prime # |
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[ 1 : max prime ]BOOL prime; |
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prime[ 1 ] := FALSE; prime[ 2 ] := TRUE; |
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FOR i FROM 3 BY 2 TO UPB prime DO prime[ i ] := TRUE OD; |
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FOR i FROM 4 BY 2 TO UPB prime DO prime[ i ] := FALSE OD; |
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FOR i FROM 3 BY 2 TO ENTIER sqrt( max prime ) DO |
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IF prime[ i ] THEN FOR s FROM i * i BY i + i TO UPB prime DO prime[ s ] := FALSE OD FI |
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OD; |
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# sum the primes and test the sum # |
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INT prime sum := 0; |
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INT prime count := 0; |
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INT prime sum count := 0; |
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print( ( "prime prime", newline ) ); |
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print( ( "count prime sum", newline ) ); |
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FOR i TO max prime DO |
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IF prime[ i ] THEN |
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# have another prime # |
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prime count +:= 1; |
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prime sum +:= i; |
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# check whether the prime sum is prime or not # |
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BOOL is prime := TRUE; |
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FOR p TO i OVER 2 WHILE is prime DO |
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IF prime[ p ] THEN is prime := prime sum MOD p /= 0 FI |
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OD; |
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IF is prime THEN |
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# the prime sum is also prime # |
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prime sum count +:= 1; |
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print( ( whole( prime count, -5 ) |
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, " " |
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, whole( i, -6 ) |
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, " " |
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, whole( prime sum, -6 ) |
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, newline |
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) |
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) |
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FI |
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FI |
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OD; |
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print( ( newline |
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, "Found " |
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, whole( prime sum count, 0 ) |
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, " prime sums of primes below " |
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, whole( max prime + 1, 0 ) |
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, newline |
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) |
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) |
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END |
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</lang> |
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{{out}} |
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<pre> |
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prime prime |
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count prime sum |
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1 2 2 |
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2 3 5 |
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4 7 17 |
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6 13 41 |
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12 37 197 |
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14 43 281 |
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60 281 7699 |
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64 311 8893 |
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96 503 22039 |
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100 541 24133 |
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102 557 25237 |
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108 593 28697 |
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114 619 32353 |
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122 673 37561 |
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124 683 38921 |
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130 733 43201 |
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132 743 44683 |
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146 839 55837 |
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152 881 61027 |
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158 929 66463 |
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162 953 70241 |
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Found 21 prime sums of primes below 1000 |
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</pre> |
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=={{header|Factor}}== |
=={{header|Factor}}== |
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