Schinzel's hypothesis H  In mathematics, Schinzel's hypothesis H is a very broad generalisation of conjectures such as the twin prime conjecture named after Andrzej Schinzel. The hypothesis aims to define the possible scope of a conjecture of the nature that several sequences of the type  with values at integers formula_2 of irreducible integer-valued polynomials  should be able to take on prime number values simultaneously, for arbitrarily large integers formula_4. Putting it another way, there should be infinitely many such formula_4 for which each of the sequence values are prime numbers. Some constraints are needed on the polynomials. Schinzel's hypothesis builds on the earlier Bunyakovsky conjecture, for a single polynomial, and on the Hardy–Littlewood conjectures and Dickson's conjecture for multiple linear polynomials. It is in turn extended by the Bateman–Horn conjecture. Note that the coefficients of the polynomials need not to be integers; for example, this conjecture includes the polynomial formula_6, since it is an integer-valued polynomial. Such a conjecture requires necessary condition. For example, if we take the two polynomials formula_7 and formula_8, there is no formula_9 for which formula_10 and formula_11 are both primes. That is because one will be an even number formula_12, and the other an odd number. The main question in formulating the conjecture is to rule out this phenomenon. Thus, we should add a condition: "For every prime "p", there is an "n" such that all the polynomial values at "n" are not divisible by "p"". The arithmetic nature of the most evident necessary conditions can be understood. An integer-valued polynomial formula_13 has a "fixed divisor formula_14" if there is an integer formula_15 such that  is also an integer-valued polynomial. For example, we can say that  has 2 as fixed divisor. Such fixed divisors must be ruled out of  for any conjecture for polynomials formula_19, formula_20, since their presence is quickly seen to contradict the possibility that formula_21 can all be prime, with large values of formula_2. Therefore, the standard form of hypothesis H is that if formula_23 defined as above has "no" fixed prime divisor, then all formula_21 will be simultaneously prime, infinitely often, for any choice of irreducible integral polynomials formula_25 with positive leading coefficients.