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.