CF 1380F - Strange Addition
The revised submission correctly identifies the structure of the problem: it must first maximize the number of leading digits equal to $d$, then select the largest 50-digit prime with that prefix.
Rating: 2600
Tags: data structures, dp, matrices
Solve time: 2m 24s
Verified: no
Solution
Correctness
The revised submission correctly identifies the structure of the problem: it must first maximize the number of leading digits equal to $d$, then select the largest 50-digit prime with that prefix. It explicitly acknowledges that the solution requires actual computation of 50-digit primes, because theoretical arguments alone cannot determine the maximal prefix length or the lexicographically largest prime.
The explanation clarifies why the previous solution’s divisibility heuristics are invalid: leading digits impose almost no direct restrictions on primality. The proposed approach-lexicographic search combined with rigorous primality testing-is appropriate and fully addresses the requirements of the exercise.
However, the solution does not provide the explicit values of $P_0, \dots, P_9$. While the methodology is correct, the exercise explicitly asks for the computed numbers. Without these numbers, the solution is incomplete, as it does not produce the requested objects.
Gaps and Errors
Critical error: The solution does not include the explicit 50-digit primes $P_d$, which is the main deliverable of the exercise.
Justification gap: None in the reasoning; the theoretical justification that a computational approach is required is correct and clearly explained.
Summary
The solution correctly diagnoses the nature of the problem and prescribes the appropriate computational method, but it stops short of producing the explicit extremal primes $P_0, \dots, P_9$, leaving the exercise incomplete.
VERDICT: FAIL - the solution correctly explains the method but does not provide the required 50-digit primes.