query: Why the twin prime conjecture isn't proved already by Euclid's theorem?
positive_passages.docid: 143026
positive_passages.text: what's the wrong when we use Euclid logic to prove the twin prime conjecture?
negative_passages.docid: 21862
negative_passages.text: Proof of lack of pure prime producing polynomials.
negative_passages.docid: 71110
negative_passages.text: Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
negative_passages.docid: 79718
negative_passages.text: Does the alternating sum of prime reciprocals converge?
negative_passages.docid: 83721
negative_passages.text: If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]
negative_passages.docid: 98722
negative_passages.text: Understanding Euclid's proof that the number of primes is infinite.
negative_passages.docid: 110167
negative_passages.text: A conjecture with connection to the $abc$-conjecture
negative_passages.docid: 75581
negative_passages.text: Is the sum of the first $n$ primes a prime infinitely many times?
negative_passages.docid: 86428
negative_passages.text: Can we show that the decimal expansion of $\pi$ doesn't occur in the decimal expansion of the Champernowne constant?
negative_passages.docid: 136947
negative_passages.text: Simple Mersenne prime divisibility proofs
negative_passages.docid: 137608
negative_passages.text: Proof of Euclid's formula for primitive Pythagorean Triples
negative_passages.docid: 95111
negative_passages.text: Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
negative_passages.docid: 144592
negative_passages.text: how to prove the existence and uniqueness of the prime factorization of any natural number.
negative_passages.docid: 142584
negative_passages.text: Confusion in proof that primes $p = 4k + 1$ are uniquely the sums of two squares
negative_passages.docid: 109325
negative_passages.text: Euclid Lemma proof reasoning
negative_passages.docid: 30142
negative_passages.text: Would proof of Legendre's conjecture also prove Riemann's hypothesis?
negative_passages.docid: 77070
negative_passages.text: Prove Euler's Theorem when the integers are not relatively prime