Notice the following sequence -
Multiplication of successive primes results in a number which has a prime number again. Is this some sort of pattern or am I reading too much into it?
19 * 17 = 323 (23 is a prime number)
23 * 19 = 437 (37 is a prime number)
29 * 23 = 667 (67 is prime)
31 * 29 = 899 (89 is prime)
37 * 31 = 1147 ( 11 and 47 are primes)
41 * 37 = 1517 ( 17 is a prime)
43 * 41 = 1763 (17is a prime)
Multiplication of successive primes results in a number which has a prime number again. Is this some sort of pattern or am I reading too much into it?
19 * 17 = 323 (23 is a prime number)
23 * 19 = 437 (37 is a prime number)
29 * 23 = 667 (67 is prime)
31 * 29 = 899 (89 is prime)
37 * 31 = 1147 ( 11 and 47 are primes)
41 * 37 = 1517 ( 17 is a prime)
43 * 41 = 1763 (17is a prime)
The observation from the above:
ReplyDelete1. The prime numbers end with the odd numbers and hence the result is a odd number.
2. Note that when all the digits of the multiplying prime numbers are odd, you can form a set of prime number in the result. Example, 3 and 23, 11 and 47.
3. The result will also be prime number except that it can be divided by the two prime numbers (the multiplying numbers). As a rule, any number cannot be called as a prime number, if it is divided by numbers between 2 and 9. The result set will end with odd numbers but not with the number 5 (because if it ends with 5, it is a multiple of 5). Hence the result set can end with either 1,3,7,9. if you group the result into two digits, then there is a high probability that few could be a prime, because of the list of prime numbers between 10 and 100 is more, especially all the odd numbers between 10 and 20, except 15 is prime.