69 lines
1.7 KiB
Python
69 lines
1.7 KiB
Python
#!/usr/bin/env python3
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# The prime 41, can be written as the sum of six consecutive primes:
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#
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# 41 = 2 + 3 + 5 + 7 + 11 + 13
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#
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# This is the longest sum of consecutive primes that adds to a prime below one-hundred.
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#
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# The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953.
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#
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# Which prime, below one-million, can be written as the sum of the most consecutive primes?
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from projecteuler import sieve, timing
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@timing
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def p050() -> None:
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N = 1000000
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primes = sieve(N)
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_max = 0
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max_p = 0
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# Starting from a prime i, add consecutive primes until the
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# sum exceeds the limit, every time the sum is also a prime
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# save the value and the count if the count is larger than the
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# current maximum. Repeat for all primes below N.
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# A separate loop is used for i=2, so later only odd numbers are
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# checked for primality.
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i = 2
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j = i + 1
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count = 1
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_sum = i
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while j < N and _sum < N:
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if primes[j] == 1:
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_sum = _sum + j
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count = count + 1
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if _sum < N and primes[_sum] == 1 and count > _max:
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_max = count
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max_p = _sum
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j = j + 1
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for i in range(3, N, 2):
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if primes[i] == 1:
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count = 1
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_sum = i
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j = i + 2
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while j < N and _sum < N:
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if primes[j] == 1:
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_sum = _sum + j
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count = count + 1
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if _sum < N and primes[_sum] == 1 and count > _max:
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_max = count
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max_p = _sum
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j = j + 2
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print('Project Euler, Problem 50')
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print(f'Answer: {max_p}')
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if __name__ == '__main__':
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p050()
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