#[0]​ check out ChatGPT response for Polignac's Conjecture! 🤯 ⚡️#nostr We know that these primes are not congruent to 0, 2, 3, or 4 modulo 6. Therefore, they must be congruent to either 1 or 5 modulo 6. If all primes were congruent to 1 modulo 6, then there would be no prime pairs with a difference of 2, as both primes would be odd. However, if all primes were congruent to 5 modulo 6, then they would alternate between being 2 more or 2 less than a multiple of 6. This would imply the existence of infinitely many prime pairs with a difference of 2, supporting Polignac's Conjecture.

Flank Steak Pizza! 🥩 🍕 Refreshing old skills.. 😋 🤙

Who is behind apple 📲🍎 I wonder? 🤔 maybe the same people that want to destroy #BTC 🤔 💭

I just captured this! 🤯⚡️ zap ⚡️ zap ⚡️ zap #nostr #BTC

#[0]​ check out this CHAT GPT proof for the twin prime conjecture for P>5(mod6) There are infinitely many prime numbers. This is a well-known result proven by the ancient Greek mathematician Euclid around 300 BCE. Euclid's proof is based on a technique called "proof by contradiction." Assume that there are finitely many prime numbers, and let's denote them as p1, p2, p3, ..., pn. Now, consider the number N = p1 * p2 * p3 * ... * pn + 1. This number N is greater than any of the primes we initially listed. Now, N can either be a prime number itself or composite. If N is prime, then it contradicts our assumption that we had listed all prime numbers up to pn. If N is composite, it must have prime factors. However, none of the primes p1, p2, ..., pn can be a factor of N because dividing N by any of them leaves a remainder of 1. This means that N has a prime factor that is not on our initial list, contradicting our assumption that we had all primes. Since assuming a finite number of primes leads to a contradiction, we conclude that there must be infinitely many prime numbers. Now let's discuss why there are infinitely many prime numbers congruent to 1 (mod 6) and infinitely many prime numbers congruent to 5 (mod 6). Suppose we consider the product of prime numbers that are congruent to 1 (mod 6). For example, we can take the primes 7, 13, 19, 31, and so on. The product of these primes will also be congruent to 1 (mod 6). This is because multiplying numbers congruent to 1 (mod 6) will always result in a number congruent to 1 (mod 6). Similarly, if we consider the product of prime numbers that are congruent to 5 (mod 6), such as 5, 11, 17, 23, and so on, the product will also be congruent to 5 (mod 6). This is because multiplying numbers congruent to 5 (mod 6) will always result in a number congruent to 5 (mod 6). Since there are infinitely many prime numbers, and we can always find more primes congruent to 1 (mod 6) and primes congruent to 5 (mod 6), it follows that there are infinitely many such products congruent to 1 (mod 6) and infinitely many products congruent to 5 (mod 6). Therefore, both the product of primes congruent to 1 (mod 6) and the product of primes congruent to 5 (mod 6) are infinite.

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#[0]​ make Damus Web resistant (Tor) like Telegram Web…we got our 🔑 keys 🔐 no one can take that away from us! Fight back! 💪 F… apple or google ⚡️ zap tyranny back ⚡️

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Good night Everyone! #[1]​ included! #nostr #hug

#ElectronicGems 💎 #nostralgic HOME - Resonance

Neon Lights Lenses 🖼️ #nightcafe.studio #art

Almost there..All Blockchain synchronized 552 GB ,next step config of RTL and open channel ⚡️ Big Thanks to🙏 #[1]​ #BTC #nostr #zap

Finishing touches on this ⚡️ NODE! #Nostr #bitcoin #Lightning

Happy Friday!🥂 🍻 🍹 💿 🎶 #nostr ❤️ 🕺

#[0]​ ​ Hi! Question: what is the best OS and software for a Lighting NODE ? And what are the recommendation/requirements for the hardware of the lighting NODE?

God 🙏 Morning everyone!