Problems & Puzzles: Puzzles

Puzzle 246.  The worms

101232121 is a prime p such that:

• abs(D_i – D_i+1)=1, for each 1<=i<L; Di is any digit of p
• ∑(D_i-D_i+1)=0, where the sum is for i=1 to L-1 (or, if you prefer a simpler statement D₁=D_L)
• L is the quantity of digits of p.

Find: 

a)      The earliest pandigital prime p of this kind

Solution:

J. K. Andersen and Jon Wharf got the solution to both questions:

a) 7654321012345678987

b) (10^978-1)/99*10^24+12123456789876543210121 = (10^1002-1)/99+2022446688866442200020 = 1010101......01012123456789876543210121

Faride Firoozbakht also found a).

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