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As you are multiplying by 4 and then adding 1, the next number is 1365.
341 is not a prime number. Prime numbers are defined as numbers which can be divided by 1 and themselves. 341 can be divided by 11 and 31 in addition to 1 and iteslf. Hence, 341 is not a prime number.
As a sequence, you multiply by 4 and add 1.
172 341 001 431
Any number that you choose can be the next number. It is easy to find a rule based on a polynomial of order 4 such that the first four numbers are as listed in the question followed by your chosen number in the next place. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.One possible solution, using a polynomial of order 3, isU(n) = 39*n^3 - 210*n^2 + 373*n - 197 for n = 1, 2, 3, 4, 5 which gives U(5) = 1293.