Prime Divisors Positive Difference

Number Theory Level 5

For a composite positive integer xx, denote by pd(x)pd(x) the smallest positive difference between any two prime divisors of x.x. Find the smallest possible value of pd(x)pd(x) for composite xx of the form x=n100+n99+⋯+n+1,x=n^{100}+n^{99}+\cdots+n+1, where nn is a positive integer.

Details and assumptions

You may refer to a list of primes.

For example, since 429=3×11×13 429 = 3 \times 11 \times 13, pd(429)=∣13−11∣=2 pd(429) = | 13 - 11 | = 2 .

Calvin Lin by Calvin Lin
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