What is the least positive integer that cannot be written as the difference between two positive primes?
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NOTE: since all primes except 2 are odd, and odd−even = odd, the only odd numbers that can be written as the difference of two primes are of the form: p − 2, where p is an odd prime.
1 = 3−2
3 = 5−2
5 = 7−2
9 = 11−2
The smallest odd positive integer that cannot be written as the difference of two positive primes is 7. We can show that this is also the smallest positive integer that cannot be written this way by showing that 2, 4, and 6 can:
2 = 5−3
4 = 7 − 3
6 = 11 − 5
P.S. Since there are infinitely many odd primes, and odd−odd = even, I suspect that any even number can be written as the difference of two primes. However we just needed to show that 2, 4, and 6 could be written this way.
ANSWER: 7
1 = 3−2
3 = 5−2
5 = 7−2
9 = 11−2
The smallest odd positive integer that cannot be written as the difference of two positive primes is 7. We can show that this is also the smallest positive integer that cannot be written this way by showing that 2, 4, and 6 can:
2 = 5−3
4 = 7 − 3
6 = 11 − 5
P.S. Since there are infinitely many odd primes, and odd−odd = even, I suspect that any even number can be written as the difference of two primes. However we just needed to show that 2, 4, and 6 could be written this way.
ANSWER: 7
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Clearly 1, 2, 3, 4, 5, and 6 can each be the difference of two positive primes:
1 = 3 - 2
2 = 5 - 3
3 = 5 - 2
4 = 7 - 3
5 = 7 - 2
6 = 11 - 5.
However, 7 cannot be the difference of two positive primes.
If two positive primes are to differ by 7, then since 7 is odd, one of these primes would have to be even while the other one is odd. Since 2 is the only even positive prime, one of the positive primes would have to be 2, and the other positive prime would have to be 2+7=9 which is impossible since 9 is not a prime (because 9=3*3).
So the least positive integer that cannot be written as the difference between two positive primes is 7.
May Jesus richly bless you today!
1 = 3 - 2
2 = 5 - 3
3 = 5 - 2
4 = 7 - 3
5 = 7 - 2
6 = 11 - 5.
However, 7 cannot be the difference of two positive primes.
If two positive primes are to differ by 7, then since 7 is odd, one of these primes would have to be even while the other one is odd. Since 2 is the only even positive prime, one of the positive primes would have to be 2, and the other positive prime would have to be 2+7=9 which is impossible since 9 is not a prime (because 9=3*3).
So the least positive integer that cannot be written as the difference between two positive primes is 7.
May Jesus richly bless you today!
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7, since 2 is the only even prime, and 9 is not prime.
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The answer is 7. I'm 14 years old, you're welcome.