229 & 233
Let the numbers be n, n-1, n+1, n-2, n+2, n-3,n+3. Sum = 7n = 1617 --> n = 231 The numbers are = 228, 229, 230, 231, 232, 233, 234 Out of these, 229 and 233 are prime.
Find the sum of all the prime numbers larger than 2 less than 10^12 that are 1 more than a perfect square. Because the number can get pretty big provide the answer mod 1007.
Note: Problem shouldn't take much more than one minute if your answer is taking too long consider looking for optimizations.
First 17 positive integers (1..17) are rearranged into a sequence such that the sum of any two adjacent terms is a perfect square. What is the sum of the first and last terms of this sequence?
If 1^3 + 2^3 + 3^3 = m^2 where m is also an integer. What are the next three consecutive positive integers such that the sum of their individual cubes is equal to a perfect square?
