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Any number that you choose can be the next number. It is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question followed by the chosen next number. 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.

The simplest solution, based on a polynomial of order 4 is

U(n) = (-5*n^4 + 70*n^3 - 343*n^2 + 734*n - 84)/12 for n = 1, 2, 3,, ...

and accordingly, the next number is 51.

Incidentally, the sequence is not the list of prime numbers greater than 30 because one is missing.

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Q: What the next number in this sequence 31 41 43 47 53?
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