What is the smallest positive integer that cannot occur as the difference between two positive prime numbers? Prove it.
2007-02-09 18:04:21 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Let us check
3-2 = 1 one is not the answer
5-3 = 2 one is not the answer
5-2 = 3 one is not the answer
7-3 = 4 one is not the answer
7-2 = 5 one is not the answer
11-5=6 one is not the answer
Now for 7
11-2 = 9, 9 > 7
Since 2 is the only even prime number difference between any other prime numbers will an even integer.
We will get a difference of 2 only if we subtract an even number from these prime number which not possible.
Therefor answer is 7
2007-02-09 18:20:26 · answer #1 · answered by Rhul s 2 · 1⤊ 0⤋
Prime integers (first 30)
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, and 113
7 is the anser, since the only even prime number is 2, and 9 is not a prime number, no positive prime numbers can have a difference of 7. Also, two odd numbers will always have a difference of an even number.
2007-02-09 18:17:06 · answer #2 · answered by Kaotik29 4 · 1⤊ 0⤋
2 is the smallest positive integer.
Proof: Assume that 1 is the smallest. Then n is prime AND n+1 is prime. But that is impossible because either n is an even number and divisible by 2 OR n+1 is an even number and divisible by 2 and a number that is divisible by 2 is not prime.
2007-02-09 18:20:11 · answer #3 · answered by Anonymous · 0⤊ 0⤋
start by process of elimination
1, 2, 3, 4, 5, 6, 7
must be seven, it's easy to show counter examples for 1 thru 6
2 + 7 = 9 that's not prime
the remaining primes are odd
an odd (prime) plus another odd (7) = an even
2007-02-09 18:13:59 · answer #4 · answered by Anonymous · 2⤊ 0⤋
It is 0
2007-02-09 18:19:05 · answer #5 · answered by Sagar Shah 1 · 1⤊ 1⤋
good question!
after some work i got it as 7.
2007-02-09 18:22:24 · answer #6 · answered by Charu Chandra Goel 5 · 0⤊ 0⤋
Tammi D is correct.Way to go Tammi.
2007-02-09 18:17:51 · answer #7 · answered by Alex 1 · 0⤊ 0⤋
~You can't make me prove it . Nyaaa Nyaaaaaaaa nyaaaaa nyaaaaaa.
2007-02-09 18:08:42 · answer #8 · answered by Oscar Himpflewitz 7 · 0⤊ 3⤋
zero. Can't be ******* proven it
2007-02-09 18:11:27 · answer #9 · answered by Anonymous · 0⤊ 3⤋