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chhitiz
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is there any other general form of prime no.s known except 6n+/-5 and 6n+/-1. is there any general form of n such that 6n+/-5 or 6n+/-1 is a composite no.?
chhitiz said:is there any other general form of prime no.s known except 6n+/-5 and 6n+/-1.
chhitiz said:is there any general form of n such that 6n+/-5 or 6n+/-1 is a composite no.?
CRGreathouse said:n in {1, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 24, 25, ...}
.
chhitiz said:but, then, if i am not wrong, this series doesn't have a pattern, does it?
chhitiz said:i have no idea what that line between n and k stands for.
chhitiz said:let me rephrase my original question- is there any general form/set of forms an+/-b which expresses every prime no. exhaustively, barring the cases where n=ck+/-d where a,b,c,d are constants and n,k integers>=0. i repeat again, this set of forms should represent every prime no. exhaustively.
chhitiz said:a^2 + b^2 + c^2 + d^2 for a, b, c, and d integers.
but then if a=b=c=d=1, we get 4. how is this prime?
chhitiz said:and, is it r^(2+pi/2) or r^2+pi/2
chhitiz said:i'm not sure but i think i found a set of 8 forms an+b which express every prime except 2,3,5.
chhitiz said:and each of these forms have exceptions, ie values of n for which no. is composite, based on integer solutions of set of quadratic eqns in two variables.
chhitiz said:is this a new approach or has someone already done this?
chhitiz said:ps- what is sieve of what's-his-face?
The general form of a prime number is 6n + 1 or 6n - 1, where n is a positive integer. This means that all prime numbers can be expressed as either one more or one less than a multiple of 6.
To determine if a number is prime using its general form, you can plug the number into the formula 6n + 1 or 6n - 1. If the resulting number is divisible by any number other than 1 and itself, then the original number is not prime. If the resulting number is not divisible by any number other than 1 and itself, then the original number is prime.
No, not all prime numbers can be expressed in the general form of 6n + 1 or 6n - 1. There are some exceptions, such as 2 and 3, which are prime but do not fit this form.
No, the general form of prime numbers cannot be used to find all prime numbers. While it can help identify some prime numbers, there are many other prime numbers that do not fit this form and would be missed.
There is no specific pattern or rule for the general form of prime numbers. It is simply a useful formula that can help identify some prime numbers, but it does not apply to all prime numbers.