Postulado de Bertrand

5 Comentarios

1. Haskell

   import Data.Numbers.Primes import Test.QuickCheck siguientePrimo :: Integer -> Integer siguientePrimo n = head [x | x <- dropWhile (<= n) primes] prop_bertrand :: Integer -> Property prop_bertrand n = n > 1 ==> n < p && p < 2*n where p = siguientePrimo n -- quickCheck prop_bertrand -- +++ OK, passed 100 tests; 150 discarded.

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   import Data.Numbers.Primes import Test.QuickCheck   siguientePrimo :: Integer -> Integer siguientePrimo n = head [x | x <- dropWhile (<= n) primes]   prop_bertrand :: Integer -> Property prop_bertrand n = n > 1 ==> n < p && p < 2*n     where p = siguientePrimo n   -- quickCheck prop_bertrand -- +++ OK, passed 100 tests; 150 discarded.

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2. Haskell

   import Data.Numbers.Primes (isPrime) import Test.QuickCheck siguientePrimo :: Integer -> Integer siguientePrimo n = head [p | p <- [n+1..], isPrime p] prop_Bertrand :: Integer -> Property prop_Bertrand n = n > 1 ==> n < p && p < 2*n where p = siguientePrimo n -- λ> quickCheck prop_Bertrand -- +++ OK, passed 100 tests.

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   import Data.Numbers.Primes (isPrime) import Test.QuickCheck siguientePrimo :: Integer -> Integer siguientePrimo n = head [p | p <- [n+1..], isPrime p] prop_Bertrand :: Integer -> Property prop_Bertrand n = n > 1 ==> n < p && p < 2*n   where p = siguientePrimo n -- λ> quickCheck prop_Bertrand -- +++ OK, passed 100 tests.

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3. Haskell

   import Data.Numbers.Primes (primes) import Test.QuickCheck siguientePrimo :: Integer -> Integer siguientePrimo n = head (dropWhile (<=n) primes) postulado_Bertrand :: Integer -> Property postulado_Bertrand n = n > 1 ==> n < p && p < 2*n where p = siguientePrimo n -- λ> quickCheck postulado_Bertrand -- +++ OK, passed 100 tests

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   import Data.Numbers.Primes (primes) import Test.QuickCheck siguientePrimo :: Integer -> Integer siguientePrimo n = head (dropWhile (<=n) primes) postulado_Bertrand :: Integer -> Property postulado_Bertrand n = n > 1 ==> n < p && p < 2*n   where p = siguientePrimo n -- λ> quickCheck postulado_Bertrand -- +++ OK, passed 100 tests

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4. Haskell

   import Data.Numbers.Primes import Test.QuickCheck -- a) siguientePrimo :: Integer -> Integer siguientePrimo n = head (filter (> n) primes) -- b) post_bertrand :: Integer -> Property post_bertrand n = n > 1 ==> n < p && p < 2*n where p = siguientePrimo n

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   import Data.Numbers.Primes import Test.QuickCheck   -- a) siguientePrimo :: Integer -> Integer siguientePrimo n = head (filter (> n) primes)   -- b) post_bertrand :: Integer -> Property post_bertrand n = n > 1 ==> n < p && p < 2*n   where p = siguientePrimo n

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5. Haskell

   import Test.QuickCheck siguientePrimo :: Integer -> Integer siguientePrimo n = head [x | x <- [n+1..], esPrimo x] esPrimo :: Integer -> Bool esPrimo n = divisores n == [1,n] divisores :: Integer -> [Integer] divisores n = [x | x <- [1..n], mod n x == 0] prop_bertrand :: Integer -> Property prop_bertrand n = n > 1 ==> n < p && p < 2*n where p = siguientePrimo n -- quickCheck prop_bertrand -- +++ OK, passed 100 tests.

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   import Test.QuickCheck   siguientePrimo :: Integer -> Integer siguientePrimo n = head [x | x <- [n+1..], esPrimo x]   esPrimo :: Integer -> Bool esPrimo n = divisores n == [1,n]   divisores :: Integer -> [Integer] divisores n = [x | x <- [1..n], mod n x == 0]   prop_bertrand :: Integer -> Property prop_bertrand n = n > 1 ==> n < p && p < 2*n   where p = siguientePrimo n   -- quickCheck prop_bertrand -- +++ OK, passed 100 tests.

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