# What does it mean if the twin prime conjecture is true or false?

From what I understand, the main premise of the twin prime conjecture is "Are there an infinite number of twin primes?" And twin primes are prime numbers that are separated by two. Examples include: $$(3,5), (5,7), (11,13), (17,19)... (793517,793519), (793787,793789), (793841,793843)... (2924351,2924353), (2924567,2924569), (2924921,2924923)... (7120187,7120189), (7120277,7120279)... (12382691,12382693), (12382691,12382693)... (16148159,16148161)... (17355509,17355511)... (18409199,18409201)$$, etc.

If I have something wrong, please tell me. If I have it correct, please explain to me why this matters. What I mean by why it matters, is what effect will it have on the real world. Usually when I hear of the practicality of prime numbers, it is in reference to cryptography. So, if there are an infinite number of twin primes, does this mean good for white hats, bad for black hats? And what if there are not an infinite number of primes and we learn them all. What implications will that have in the real world. Does the importance of the twin prime conjecture go beyond cryptography? If so, please explain. Thank you.

• It's a very simple question that's been asked for two and a half millennium, and still no one knows the answer. Wouldn't you find that intriguing? Jun 4, 2021 at 9:20
• It kills me how I have two answers AND a comment on this question, but NOBODY has upvoted the question. So people think it's worthy of an answer or comment, but not worthy to be upvoted. How does that work? Jun 4, 2021 at 19:53
• The ways of the upvote fairies (and the downvote fairies as well) are ineffable, unfortunately. Jun 4, 2021 at 20:28
• @JimmyG. What are you going to do with the upvotes or downvotes as you say that you don't care whether the number of twin primes is finite or infinite. Jun 4, 2021 at 23:16
• @JimmyG. HAHAHAHAHAAAAAA!!! I know. Tough crowd. Oct 25, 2021 at 20:06