The expression 2^33-2^19-2^17-1 evaluates as:
85, 892,792,313
The prime factorization of 85,892, 792, 313 is:
(3^2)*13*661*37021
So, none of the prime factors of given expression is located between 1000 and 5000.
Accordingly, the said divisor must be composite.
Then, there are only two possibilities: 13*661 or, 3*661
13*661= 8593, which does NOT lie between 1000 and 5000
3*661 = 1983, which does lie between 1000 and 5000.
Consequently, 1983 is the required divisor lying between 1000 and 5000.
*** I hope to posit a fully analytical solution to this in future.
Edited on June 2, 2022, 4:50 am
Puzzle Solution
