Find the only sequence of 5 prime numbers that have a common difference of 6
a b c d e
b - a = 6
c - b = 6
d - c = 6
. . . . .
Prove that it is the only one, there is no other sequence like it.
a b c d e
b - a = 6
c - b = 6
d - c = 6
. . . . .
Prove that it is the only one, there is no other sequence like it.
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e = a + 4*6
e = a + 24
d = a + 18
c = a + 12
b = a + 6
a must be prime, so 2 is even and therefore all the others will be composite.
a = 3 makes all the numbers be divisible by 3, so that is not possible.
a = 5 is good and then you'd have a sequence such as 5, 11, 17, 23, and 29.
e = a + 24
d = a + 18
c = a + 12
b = a + 6
a must be prime, so 2 is even and therefore all the others will be composite.
a = 3 makes all the numbers be divisible by 3, so that is not possible.
a = 5 is good and then you'd have a sequence such as 5, 11, 17, 23, and 29.
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5-11-17-23-29
This could be the only one, because any such sequence must include a number with 5 in the ones place. Since 5 is the only such number that is prime, this is the only possible sequence.
This could be the only one, because any such sequence must include a number with 5 in the ones place. Since 5 is the only such number that is prime, this is the only possible sequence.