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It is proved that there are infinitely many prime numbers of type 4k-1 I'm studying and researching the mathematical thought of group theory and studying Zhang Guangxiang's book. I can't do this exercise I believe that the essence of mathematical research is no different from other knowledge. The key point of problem solving lies in the depth of our understanding of existing simple and similar problems. In fact, there are many examples to illustrate the essential characteristics and laws of an abstract concept. Mathematicians need to study every aspect carefully in order to deeply grasp a concept, thought and method I'm not a professional mathematician, and I lack this kind of environment and energy. But I'm born with a very deep understanding and passion for mathematics. For example, group, such concepts and ideas are really amazing I want 4k-1, not 4K + 1. For example, 7 is not 4K + 1. My knowledge of number theory is very limited,
Proof: the counter proof assumes that there are finite primes of type 4k-1, no matter n, P1, P2 PN let a = (P1 * P2 *...) PN) ^ 2 + 2 due to (P1 * P2 * If a is a prime, then a is a prime of type 4k-1, and it is not contradictory among the N primes. If a is a composite number, it is obvious that there must be a contradiction in the prime factor of A
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