Find ‘clean’ arithmetic progressions (AP) of integers such that all its terms are divisible by a twin prime product. Clean here means that no other integer lying between the terms of the AP, is divisible by a twin prime product.
Very large integers, sometimes of the order of millions of digits, which are impossible to completely factorize via the known general factorization algorithms. Even partial factorizations are very difficult. For these integers we apply special factorization methods to achieve a partial factorization. The interest lies not only in the prime divisors themselves, but in the methods used.
We consider algebraic expressions whose values are integers in a specified domain, that can be factored into algebraic factors whose values are also integers. The results are integer divisors of the original integer, although not necessarily prime divisors.
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