Many problems in Project Euler relate to working with primes. I use primesieve-python to help solve such problems. It consists of Python bindings for the primesieve C++ library. Generates primes orders of magnitude faster than any pure Python code. Features:

- Generate a list of primes
- Count primes and prime k-tuplets
- Print primes and prime k-tuplets
- Find the nth prime
- Iterate over primes using little memory

Anyway, here’s Problem 50 from Project Euler:

Here’s how I did it:

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# Question: Which prime, below one-million, can be written as the sum of the most consecutive primes | |

from primesieve import * | |

from math import * | |

# Generate list of primes under a million | |

primes_under_million = generate_primes(10**6) | |

# Sum of consecutive primes is of order 0.5(n^2)(logn) | |

# Calculate 'n' so that sum of consecutive primes is less than a million (and not necessarily prime) | |

nsum = 1 | |

n = 1 | |

while nsum < 10**6: | |

nsum = 0.5*(n**2)*(log(n, e)) | |

n += 1 | |

# Calculate index so that sum of first 'index' consecutive primes is under a million and also prime | |

primes_subset = primes_under_million[:n] | |

nsum = sum(primes_under_million[:n]) | |

while nsum > 10**6: | |

n -= 1 | |

nsum = sum(primes_under_million[:n]) | |

primes_sum = 0 | |

index = 0 | |

for i in range(len(primes_subset)): | |

if i % 2 == 1: | |

pass | |

else: | |

sumprimes = sum(primes_subset[:i]) | |

if sumprimes > primes_sum and sumprimes < 10**6 and sumprimes in primes_under_million: | |

primes_sum = sumprimes | |

index = i | |

# Print out sum of consecutive primes till 'index', index, n | |

# print primes_sum, index, n | |

# Check consecutive primes within a range (index to n) such that their number is greater than index and maximum | |

j = index + 1 | |

start = 0 | |

while j <= n: | |

while (j-start) >= (n-index): | |

sumprimes = sum(primes_subset[start:j]) | |

if sumprimes > primes_sum and sumprimes in primes_under_million: | |

primes_sum = sumprimes | |

start += 1 | |

j += 1 | |

start = 0 | |

print primes_sum | |

**Answer:** *997651*