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max prime that divides S = p_1 + p_2 + p_3 + ...+ p_ {999}, product of digits

Source: Mathematics Regional Olympiad of Mexico Center Zone 2008 P5

November 9, 2021
number theoryProductDigitsdivides

Problem Statement

Each positive integer number n ge1n \ ge 1 is assigned the number pnp_n which is the product of all its non-zero digits. For example, p6=6p_6 = 6, p32=6p_ {32} = 6, p203=6p_ {203} = 6. Let S=p1+p2+p3+⋯+p999S = p_1 + p_2 + p_3 + \dots + p_ {999}. Find the largest prime that divides SS .
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