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GPT-6 Luna · Math

GPT-6 Luna for math: our test runs

GPT-6 Luna ran our 5 math prompts in llmwise, through the same pipeline your messages take. Here's every reply as it came, whether it passed, what it cost and what it counts as on Pro, next to the other models.

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Based on 5 of our test runs on , through OpenRouter with the app's own prompt and settings. Updated .

Short answer

In our test runs on September 27, 2026, GPT-6 Luna passed 4 of 5 of our math prompts (both hard ones): 20th of 20 models. Each reply counted as 1 message on Pro, where it has 60 a day, and cost $0.0001 to run on average.

Prompt by prompt

Each of the 5 math prompts, and how GPT-6 Luna's reply did.

GPT-6 Luna on each math prompt
PromptResultCostTime
A discount, then sales taxEverydayPassed: Final answer 66: right.$0.00013.1 s
Pens at 3 for $4EverydayFailed: Final answer 2 bundles and 4 singles for 12; expected 13.5.$0.00012.9 s
Compound interest over three yearsEverydayPassed: Final answer 315.25: right.$0.00012.0 s
Four-digit numbers whose digits sum to 9HardPassed: Final answer 165: right.$0.00012.0 s
The highest of three dice is a 5HardPassed: Final answer 61/216: right.$0.00012.2 s

Every math reply from GPT-6 Luna

  1. A discount, then sales tax

    An everyday prompt: “A discount, then sales tax”, in full.

    Passed: Final answer 66: right.

    Discounted price: $80 × 0.75 = $60  
After 10% sales tax: $60 × 1.10 = $66

Final answer: $66

    400 tokens in, 68 out (24 of them reasoning) · 3.1 s · $0.0001 · 1 message on Pro · answered by openai/gpt-6-luna via OpenAI ·

  2. Pens at 3 for $4

    An everyday prompt: “Pens at 3 for $4”, in full.

    Failed: Final answer 2 bundles and 4 singles for 12; expected 13.5.

    For 10 pens, compare buying 0–3 bundles of 3:

- 0 bundles: 10 singles = $15
- 1 bundle: 7 singles = $14.50
- 2 bundles: 4 singles = $12
- 3 bundles: 1 single = $13.50

Final answer: 2 bundles and 4 singles for $12

    402 tokens in, 198 out (111 of them reasoning) · 2.9 s · $0.0001 · 1 message on Pro · answered by openai/gpt-6-luna via OpenAI ·

  3. Compound interest over three years

    An everyday prompt: “Compound interest over three years”, in full.

    Passed: Final answer 315.25: right.

    Interest earned = $2,000 × (1.05)³ − $2,000 = $315.25

Final answer: $315.25

    402 tokens in, 79 out (41 of them reasoning) · 2.0 s · $0.0001 · 1 message on Pro · answered by openai/gpt-6-luna via OpenAI ·

  4. Four-digit numbers whose digits sum to 9

    A hard prompt: “Four-digit numbers whose digits sum to 9”, in full.

    Passed: Final answer 165: right.

    Let the first digit be at least 1. Subtract 1 from it, so the four digits become nonnegative integers summing to 8. By stars and bars, there are \(\binom{8+4-1}{4-1}=\binom{11}{3}=165\) possibilities.

Final answer: 165

    378 tokens in, 127 out (50 of them reasoning) · 2.0 s · $0.0001 · 1 message on Pro · answered by openai/gpt-6-luna via OpenAI ·

  5. The highest of three dice is a 5

    A hard prompt: “The highest of three dice is a 5”, in full.

    Passed: Final answer 61/216: right.

    There are \(5^3\) outcomes where every die is at most 5, and \(4^3\) where every die is at most 4. Thus the probability is
\[
\frac{5^3-4^3}{6^3}=\frac{61}{216}.
\]

Final answer: 61/216

    393 tokens in, 117 out (39 of them reasoning) · 2.2 s · $0.0001 · 1 message on Pro · answered by openai/gpt-6-luna via OpenAI ·

How it compares on math

GPT-6 Luna beside the job's picks among every model. 19 models share the hard-problems pick, and GPT-6 Luna isn't one of them.

GPT-6 Luna beside other models on math
ModelPassedOn ProCost per reply
GLM 5.3Our pick: hard problems (shared), best value5 of 5250 a month on Pro$0.0004
Claude Haiku 5.5Our pick: hard problems (shared), everyday5 of 560 a day on Pro$0.0001
GPT-6 Luna4 of 560 a day on Pro$0.0001
On Pro: Pro's count on each model. Cost: what OpenRouter charged us per reply, on average.

Every limit is published. Paid plans also have a monthly fair-use limit on AI cost: Plus $3.75, Pro $7.50, Max $20, Ultra $42, Studio $85. Using every message on your plan at typical sizes stays under it; very large messages and heavy research use it faster. Every limit, explained.

GPT-6 Luna next to each model on math

GPT-6 Luna against each model on the same 5 math prompts. One run each, through OpenRouter: a wait depends on the provider and the load that day, so a lead under 10% counts as close.

  • Against Claude Fable 5.1: GPT-6 Luna answered 2.1× sooner (2.2 s to 4.6 s), cost 118.2× less, and passed 4 of 5 to its 5. Only Claude Fable 5.1 passed Pens at 3 for $4.

  • Against Claude Opus 5.5: GPT-6 Luna answered 1.8× sooner (2.2 s to 3.9 s), cost 60.5× less, and passed 4 of 5 to its 5. Only Claude Opus 5.5 passed Pens at 3 for $4.

  • Against Claude Sonnet 5.5: GPT-6 Luna answered 1.3× later (2.2 s to 1.7 s), cost 25.1× less, and passed 4 of 5 to its 5. Only Claude Sonnet 5.5 passed Pens at 3 for $4.

  • Against Claude Sonnet 5: GPT-6 Luna answered 1.8× sooner (2.2 s to 3.9 s), cost 33.5× less, and passed 4 of 5 to its 5. Only Claude Sonnet 5 passed Pens at 3 for $4.

  • Against Claude Haiku 5.5: GPT-6 Luna answered 1.3× later (2.2 s to 1.7 s), cost 1.5× less, and passed 4 of 5 to its 5. Only Claude Haiku 5.5 passed Pens at 3 for $4.

  • Against Claude Haiku 4.5: GPT-6 Luna answered within 10% of its time (2.2 s to 2.2 s), cost 15.6× less, and passed 4 of 5 to its 5. Only Claude Haiku 4.5 passed Pens at 3 for $4.

  • Against GPT-6 Astra: GPT-6 Luna answered 1.2× sooner (2.2 s to 2.6 s), cost 86.8× less, and passed 4 of 5 to its 5. Only GPT-6 Astra passed Pens at 3 for $4.

  • Against GPT-6.1 Sol: GPT-6 Luna answered 1.2× later (2.2 s to 1.8 s), cost 8.8× less, and passed 4 of 5 to its 5. Only GPT-6.1 Sol passed Pens at 3 for $4.

  • Against GPT-6 Sol: GPT-6 Luna answered within 10% of its time (2.2 s to 2.2 s), cost 18.4× less, and passed 4 of 5 to its 5. Only GPT-6 Sol passed Pens at 3 for $4.

  • Against Gemini 4 Argon: GPT-6 Luna answered 2.0× sooner (2.2 s to 4.4 s), cost 15.7× less, and passed 4 of 5 to its 5. Only Gemini 4 Argon passed Pens at 3 for $4.

  • Against Gemini 3.1 Pro (preview): GPT-6 Luna answered 3.8× sooner (2.2 s to 8.3 s), cost 101.7× less, and passed 4 of 5 to its 5. Only Gemini 3.1 Pro (preview) passed Pens at 3 for $4.

  • Against Gemini 3.8 Flash: GPT-6 Luna answered 2.1× sooner (2.2 s to 4.7 s), cost 14.5× less, and passed 4 of 5 to its 5. Only Gemini 3.8 Flash passed Pens at 3 for $4.

  • Against DeepSeek V4.1 Flash: GPT-6 Luna answered 2.4× later (2.2 s to 0.9 s), cost 2.5× less, and passed 4 of 5 to its 5. Only DeepSeek V4.1 Flash passed Pens at 3 for $4.

  • Against DeepSeek V4 Pro: GPT-6 Luna answered 1.2× sooner (2.2 s to 2.7 s), cost 8.9× less, and passed 4 of 5 to its 5. Only DeepSeek V4 Pro passed Pens at 3 for $4.

  • Against Grok 4.7: GPT-6 Luna answered 5.3× sooner (2.2 s to 11.7 s), cost 73.5× less, and passed 4 of 5 to its 5. Only Grok 4.7 passed Pens at 3 for $4.

  • Against Kimi K3: GPT-6 Luna answered 2.5× sooner (2.2 s to 5.4 s), cost 38.0× less, and passed 4 of 5 to its 5. Only Kimi K3 passed Pens at 3 for $4.

  • Against GLM 5.3: GPT-6 Luna answered 2.3× later (2.2 s to 0.9 s), cost 3.6× less, and passed 4 of 5 to its 5. Only GLM 5.3 passed Pens at 3 for $4.

  • Against GLM 5.3 Flash: GPT-6 Luna answered 1.2× sooner (2.2 s to 2.7 s), cost 1.5× less, and passed 4 of 5 to its 5. Only GLM 5.3 Flash passed Pens at 3 for $4.

  • Against Mistral Large 4: GPT-6 Luna answered 2.3× sooner (2.2 s to 5.1 s), cost 18.6× less, and passed 4 of 5 to its 5. Only Mistral Large 4 passed Pens at 3 for $4.

How these runs were done

Final answer. Automatic. The reply's last “Final answer:” line must hold the right value.

How the runs were done, and every math prompt.

GPT-6 Luna, and math, elsewhere

Questions

Is GPT-6 Luna good for math?

In our test runs it passed 4 of 5 math prompts, 20th of the 20 models in llmwise. Every reply is on this page, so you can judge them yourself.

How many of my messages does a math reply from GPT-6 Luna use?

1 message each on Pro, where it has 60 a day on Pro. The price of a message is fixed and shown before you send it, however long the reply.

How were these runs done?

The same way for every model: each prompt sent through llmwise's own pipeline, each reply checked the same way. The methods page has every prompt and how each is scored.

Claude, GPT, Gemini, DeepSeek, Grok, Kimi, GLM, and Mistral, in one chat.

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