The twin primes (those with a difference of just 2) up to 1000, are as follows:
3, 5
5, 7
11,13
17, 19
29, 31
41, 43
59, 61
71, 73
101, 103
107, 109
137, 139
149, 151
179, 181
191, 193
197, 199
227, 229
239, 241
269, 271
281, 283
311, 313
347, 349
419, 421
431, 433
461, 463
521, 523
569, 571
599, 601
617, 619
641, 643
659, 661
809, 811
821, 823
827, 829
857, 859
881, 883
The first twin primes after 1000 are 1019 and 1021.
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Actually, 13 and 15 are not twin primes because twin primes are pairs of prime numbers that have a difference of 2 between them. In this case, 13 is a prime number, but 15 is not a prime number because it can be divided by 3 and 5 in addition to 1 and itself. Therefore, 13 and 15 do not meet the criteria to be considered twin primes.
Yes, all primes over three are either of the form 6n - 1 or 6n + 1. So the only way for them to be prime pairs is for one to be of the same n, one -1 and the other +1; so the number between them is always of the form 6n, and thus always divisible by six.
Any number greater than one can be co-prime. I guess the answer is 49.
Euclid proved there are infinite. He said that if there were a finite number of primes, if you multiply all the primes together and then add 1, the result will be a prime. Thus, there are infinite primes.
There are some patterns, but none that can help you determine, in all cases, whether the number is a prime or not.For example: * All primes except 2 are odd numbers. However, not all odd numbers are primes. * All primes greater than 3 are of the form 6n - 1, or 6n + 1. However, not all numbers of this form are primes.