Project Euler（46）
Posted on Sunday, March 29th, 2009 at 4:43 pm by Universe QueenProblem 46:
It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
9 = 7 + 2×1^(2)
15 = 7 + 2×2^(2)
21 = 3 + 2×3^(2)
25 = 7 + 2×3^(2)
27 = 19 + 2×2^(2)
33 = 31 + 2×1^(2)It turns out that the conjecture was false.
What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
Answer: 5777
Implementation in Java:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 | public class Euler46 { public static boolean isPrime( int number ) { if( number < 2 ) { return false; } else if ( number == 2 ) { return true; } else { for( long i=2; i<=Math.sqrt(number); i++ ) { if( number%i == 0 ) { return false; } } } return true; } public static void main(String[] args) { int result = 7; boolean ok = false; while( !ok ) { result += 2; ok = true; if( isPrime( result ) ) { ok = false; continue; } for( int p=2; p<result; p++ ) { if( isPrime( p ) ) { int r = result - p; int k = r / 2; double s = Math.round( Math.sqrt(k) ); s = s * s - k; if( k*2 == r && s < 0.000001 && s > -0.000001 ) { ok = false; break; } } } } System.out.println( result ); } } |
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