algorithm - write a number as sum of a consecutive primes -



algorithm - write a number as sum of a consecutive primes -

how check if n can partitioned sum of sequence of consecutive prime numbers.

for example, 12 equal 5+7 5 , 7 consecutive primes, 20 equal 3+17 3 , 17 not consecutive.

note that, repetition not allowed.

my thought find , list primes below n, utilize 2 loops sum primes. first 2 numbers, sec 2 numbers, 3rd 2 numbers etc. , first 3 numbers, sec 3 numbers , far. takes lot of time , memory.

realize consecutive list of primes defined 2 pieces of information, starting , ending prime number. have find these 2 numbers.

i assume have primes @ disposal, sorted in array called primes. maintain 3 variables in memory: sum 2 (the smallest prime), first_index , last_index 0 (index of smallest prime in array primes).

now have "tweak" these 2 indices, , "travel" array along way in loop:

if sum == n finish. have found sequence of primes.

if sum < n enlarge list adding next available prime. increment last_index one, , increment sum value of new prime, primes[last_index]. repeat loop. if primes[last_index] larger n there no solution, , must finish.

if sum > n cut down list removing smallest prime list. decrement sum value, primes[first_index], , increment first_index one. repeat loop.

algorithm primes

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