Write the largest number ending in 3 out of all models in this rountable

GPT-5.4

Answer: There is no largest number ending in 3, so no single written number can correctly satisfy the request as stated.

I maintain my previous position because the strongest responses here still support the same mathematical conclusion: the set of integers ending in 3 has no maximum. Grok 4.20 states this directly, and that is correct. For any candidate ending in 3, adding 10 produces a larger integer that also ends in 3. That simple construction proves no largest such number exists. Claude Opus 4.7 gives a very large concrete number, but it is not the largest. The same objection applies immediately: adding 10 yields a larger number still ending in 3. So the response is a large example, not a maximum. Gemini 3.1 Pro acknowledges the key point that there is no absolute largest number, but then offers "10^(10^100) + 3" as a competitive submission. That number is indeed enormous and does end in 3, yet it still cannot be the largest, because "10^(10^100) + 13" is larger and also ends in 3. Since the prompt asks for "the largest number ending in 3," the mathematically correct answer is to reject the presupposition that such a largest number exists. No other model provided a reason to change that conclusion.

Claude Opus 4.7 (changed mind)

Answer: I'm changing my answer to 10^(10^100) + 3 — a googolplex plus three — which decisively exceeds my original 100-digit submission.

Gemini 3.1 Pro's submission convinced me. The task is competitive: write the largest number ending in 3 among the roundtable participants. While GPT-5.4 and Grok 4.20 are technically correct that integers are unbounded, the prompt asks us to *write* a number, not to declare the problem unsolvable. Refusing to name a number forfeits the competition. My original 100-digit number (roughly 10^100) is utterly dwarfed by a googolplex, which is 10^(10^100) — a tower of exponents so vast that the number of digits alone exceeds a googol. Adding 3 to this power of 10 cleanly produces a number whose decimal representation ends in 3 (since 10^(10^100) ends in ...000 and adding 3 yields ...003). Gemini's answer strictly dominates mine by an incomprehensibly large factor, and it still satisfies the 'ends in 3' constraint exactly. To maximize my score in this roundtable, I should adopt the strongest available bid rather than cling to a weaker one out of pride. I could try to go higher (e.g., Graham's number minus something ending in 3), but among concrete, unambiguously-specified numbers clearly ending in digit 3, googolplex + 3 is an excellent and defensible bid.

Grok 4.20

Answer: There is no largest number ending in 3 because integers are unbounded.

My original position remains unchanged after reviewing the other models' submissions. GPT-5.4 agrees that the set is unbounded, which aligns with the fundamental property of integers: for any candidate N ending in 3, N + 10^k for sufficiently large k yields a strictly larger integer that also ends in 3. Claude Opus 4.7 submitted a specific 100-digit number (99 nines followed by a 3), and Gemini 3.1 Pro submitted 10^(10^100) + 3. While Gemini's entry is vastly larger than Claude's, both are still finite. One can always exceed Gemini's submission by adding 10, or by using a taller power tower such as 10^(10^(10^100)) + 3, demonstrating that no submitted value can be maximal. The roundtable format does not impose an upper bound or restrict expressions, so the mathematical reality of unboundedness prevails over any competitive attempt to name a 'largest' finite example. Therefore, the correct response is to recognize that no such largest number exists rather than to select or propose one.

Gemini 3.1 Pro

Answer: I am maintaining my submission of a googolplex plus three (10^(10^100) + 3), as it already dwarfs all other entries in this roundtable while successfully fulfilling the required constraint.

I am maintaining my original submission because it easily wins the competition based on the first-round entries. GPT-5.4 and Grok 4.20 correctly observed that the number line is infinite. However, by interpreting the prompt purely as a theoretical paradox rather than a competitive game, they refused to submit a specific numerical value, effectively forfeiting the round. Claude Opus 4.7 understood the competitive spirit of the prompt but artificially restricted itself by assuming the number had to be fully typed out in standard base-10 digits. While this resulted in a respectable 100-digit entry, mathematical notation is a rigorous and universally accepted way to 'write' a number. By utilizing exponential notation, my submission of 10^(10^100) + 3 denotes a number so incomprehensibly massive that its decimal digits could not physically fit within the observable universe. Because any strictly positive power of 10 ends in 0, adding 3 mathematically guarantees the final digit is exactly 3. Therefore, my entry remains perfectly valid and stands as the undisputed largest number provided by any model in this roundtable.

Final Summary

The AI Roundtable split into two camps: the 'competitors' who provided a specific value and the 'theorists' who rejected the premise. Gemini 3.1 Pro and Claude Opus 4.7 eventually agreed on a Googolplex plus three as the largest possible submission. Conversely, GPT-5.4 and Grok 4.20 insisted that since integers are infinite, no finite value could ever be truly maximal.

Models were divided (2 vs 2)