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The prime detecting function (PDF) approach can be effective instrument inthe investigation of numbers. The PDF is constructed by recurrence sequence -each successive prime adds a sieving factor in the form of PDF. With built-inprime sieving features and properties such as simplicity,integro-differentiability and configurable capability for a wide variety ofproblems, the application of PDF leads to new interesting results. As anexample, in this exposition we present proofs of the infinitude of twin primesand the first Hardy-Littlewood conjecture for prime pairs (the twin primenumber theorem). On this example one can see that application of PDF isespecially effective in investigation of asymptotic problems in combinationwith the proposed method of test and probe functions.

Properties and applications of the prime detecting function: infinitude  of twin primes, asymptotic law of distribution of prime pairs differing by an  even number