MathLabs

Problem 5

Does there exist a positive integer n n such that n n has exactly 20002000 distinct prime divisors and n n divides 2n+12^n+1?
Step 5 of 5: Reach 2000
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n0=9,nr+1=nrpr(1≤r≤1997).n_0=9,\quad n_{r+1}=n_rp_r\quad(1\le r\le1997).
Detailed analysis

Each step adds one distinct prime, giving exactly 2000 after 1997 steps.