Question

An integer n is called the jumping champion if it is the most frequently occurring difference between consecutive primes.

Answer 1

An integer is called a jumping champion if is the most frequently occurring difference between consecutive primes (Odlyzko et al. 1999). This term was coined by J. H. Conway in 1993.

Answer 2

Answer:

• The first few primes are listed below-

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37....

• The difference between two consecutive numbers amongst these primes is as follows-

1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6.....

• In the differences given above, 2 occurs the maximum number of times. It is called as a jumping champion because it occurs most often as a gap between the primes.
• An integer n is called the jumping champion if it is the most frequently occurring difference between consecutive primes.
• The term jumping champion was coined by John Horton Conway in 1993.
• An integer that is a Jumping champion is also called a high jumper.
• Sometimes there can be more than one jumping champion because two integers can occur an equal number of times in the difference of consecutive primes.

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