Math Files(@Math_files):Euler loved calculating prime numbers. He produced tables of all the primes up to 100,000 and even a few beyond. In 1732, he was also the first to show that Fermat’s formula for primes, 2^(2^n) + 1, breaks down when n = 5. Using new theoretical ideas, he managed to factor this ten-digit number into a product of two smaller numbers. One of his most curious discoveries was a formula that seemed to generate an unusually large number of primes. In 1772, he calculated all the values obtained by substituting the numbers from 0 to 39 into the formula x² + x + 41. He obtained the following list:

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Euler loved calculating prime numbers. He produced tables of all the primes up to 100,000 and even a few beyond. In 1732, he was also the first to show that Fermat’s formula for primes, 2^(2^n) + 1, breaks down when n = 5. Using new theoretical ideas, he managed to factor this ten-digit number into a product of two smaller numbers. One of his most curious discoveries was a formula that seemed to generate an unusually large number of primes. In 1772, he calculated all the values obtained by substituting the numbers from 0 to 39 into the formula x² + x + 41. He obtained the following list: