Question 1204268: Find the two-digit prime number that is in the middle of the distance between the nearest prime number less than it, and the nearest prime number greater than it.
Found 4 solutions by greenestamps, ikleyn, MathTherapy, math_tutor2020:
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
There is no algebraic method for solving this problem. This is something that anybody, including you, can do as easily as we can.
Simply make an ordered list of all the 2-digit prime numbers and find the only place in the list where one of the primes is halfway between the primes just before and just after it.
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(later addition to my response....)
You can find the answer in a somewhat formal way by looking at the differences between successive 2-digit prime numbers. The condition will be satisfied when two consecutive differences are the same.
11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 ... (consecutive prime numbers)
2 4 2 4 6 2 6 4 2 4 6 6 2 6 4 2 6 (differences between consecutive primes)
The first two consecutive differences (of 6) are between the consecutive primes 47 and 53 and between 53 and 59, so the answer is 53.
This method of analyzing a sequence of numbers by examining the differences between successive terms of the sequence is a useful mathematical tool.
Answer by ikleyn(52879)  (Show Source):
You can put this solution on YOUR website! .
Use the table of primes
https://www.splashlearn.com/math-vocabulary/algebra/prime-number#:~:text=So%2C%20from%20the%20table%20it,numbers%20between%201%20and%20100.
and find the solution
47,  , 59.
In order for my solution be educative, I will add three observations,
that may help you to organize your search effectively:
(1) The step must be even integer number. It is obvious, since otherwise
at least one of the numbers in the sequence will be multiple of 2.
(2) The step 2 does not work. It is obvious, since otherwise
at least one of the numbers in the sequence will be multiple of 3.
(3) The step 4 does not work. It is obvious, since otherwise
at least one of the numbers in the sequence will be multiple of 3.
(4) Fortunately, the step of 6 does work, as my solution shows.
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website!
Find the two-digit prime number that is in the middle of the distance between the nearest prime number less than it, and the nearest prime number greater than it.
47, 53, 59.
Answer by math_tutor2020(3817)  (Show Source):
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