60 lines
1.6 KiB
Ruby
60 lines
1.6 KiB
Ruby
descr=%{
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Euler published the remarkable quadratic formula:
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n² + n + 41
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It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39. However, when n = 40, 40^(2) + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when n = 41, 41² + 41 + 41 is clearly divisible by 41.
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Using computers, the incredible formula n² − 79n + 1601 was discovered, which produces 80 primes for the consecutive values n = 0 to 79. The product of the coefficients, −79 and 1601, is −126479.
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Considering quadratics of the form:
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n² + an + b, where |a| < 1000 and |b| < 1000
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where |n| is the modulus/absolute value of n
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e.g. |11| = 11 and |−4| = 4
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Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n = 0.
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}
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thoughts=%{
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compute a huge number of prime and test using it
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}
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puts "read prime numbers"
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prime=File.read('firsts_10MM_primes.txt').split.collect! { |i| i.to_i }
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is_prime={}
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prime.each do |p|
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is_prime[p]=true
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end
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puts "begin computation"
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max=0
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besta=0
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bestb=0
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def is_prime_number(num,is_prime)
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if num>10000000
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puts "may an error for #{num}"
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end
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return is_prime[num]
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end
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(-1000..1000).each do |a|
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(-1000..1000).each do |b|
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n=0
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while is_prime_number( n**2 + a*n + b , is_prime)
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n+=1
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end
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if n>max
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max=n
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besta=a
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bestb=b
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puts "#{besta} #{bestb} => #{max}"
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end
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end
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end
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puts "#{besta} #{bestb} => #{max}"
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puts "product= #{besta * bestb}"
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