31 lines
1.2 KiB
Haskell
31 lines
1.2 KiB
Haskell
-- By replacing the 1st digit of the 2-digit number *3, it turns out that six
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-- of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime.
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--
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-- By replacing the 3rd and 4th digits of 56**3 with the same digit, this
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-- 5-digit number is the first example having seven primes among the ten
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-- generated numbers, yielding the family: 56003, 56113, 56333, 56443, 56663,
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-- 56773, and 56993. Consequently 56003, being the first member of this family,
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-- is the smallest prime with this property.
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--
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-- Find the smallest prime which, by replacing part of the number (not
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-- necessarily adjacent digits) with the same digit, is part of an eight prime
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-- value family.
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import Euler
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import Debug.Trace
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isPrime :: Integer -> Bool
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isPrime n = n >= 2 && all (\p -> n `mod` p /= 0) smallPrimes
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where smallPrimes = takeWhile (<= floor (sqrt (fromIntegral n))) primes
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main = print $ head $ do
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base <- primes
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let digits = toDigits base
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template <- sequenceA <$> mapM (\n -> [const n, id]) digits
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let family = nub $ filter isPrime $ map fromDigits $
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filter ((/= 0) . head) $ map template [0..9]
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guard $ take 1 family == [base]
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guard $ length family >= 8
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traceM $ show family
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return base
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