49 lines
1 KiB
Ruby
49 lines
1 KiB
Ruby
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descr=%{
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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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puts "Read primes and init data structure"
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primes=File.read("firsts_1MM_primes.txt").split().collect{|x| x.to_i }
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is_prime={}
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primes.each do |p|
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is_prime[p]=true
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end
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puts "search"
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k=1
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while true
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n=2*k+1
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k+=1
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next if is_prime[n]
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puts "* "+n.to_s if k%100 == 0
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found=false
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primes.each do |p|
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break if p>n
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i=0
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while p + 2*(i**2) <= n
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if p + 2*(i**2) == n
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# puts "#{n} = #{p} + 2.#{i}^2"
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found=true
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break
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end
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i+=1
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end
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break if found
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end
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if not found
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puts n
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exit 0
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end
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end
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