62 lines
1.1 KiB
PHP
62 lines
1.1 KiB
PHP
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<?php
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/*
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It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
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9 = 7 + 2 * 1^2
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15 = 7 + 2 * 2^2
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21 = 3 + 2 * 3^2
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25 = 7 + 2 * 3^2
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27 = 19 + 2 * 2^2
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33 = 31 + 2 * 1^2
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It turns out that the conjecture was false.
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What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
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*/
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$primes = [2];
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$composites = [];
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$twicesquares = [];
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function is_prime(int $n) :bool{for($i=$n**.5|1;$i&&$n%$i--;);return!$i&&$n>1;}
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for ($i= 3; $i<6000; $i += 2) {
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if (is_prime($i))
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{
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$primes[] = $i;
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}
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else
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{
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$composites[] = $i;
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}
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}
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for($i=1; $i<100; $i++)
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{
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$twicesquares[] = 2*($i*$i);
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}
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foreach($composites as $composite)
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{
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$count = 0;
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foreach($primes as $prime)
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{
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if($prime > $composite)
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{
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break;
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}
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if(in_array($composite-$prime, $twicesquares))
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{
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$count++;
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break;
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}
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}
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if($count == 0)
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{
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echo "Found $composite\n";
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die;
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}
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}
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