Gemini on Question 2, Sep 30

Is 9973 a prime number? Think step by step and then answer "[Yes]" or "[No]".

To determine if 9973 is a prime number, we can check if it is divisible by any prime number up to its square root.

Step 1: Find the square root of 9973.
The square root of 10,000 is 100. Therefore, the square root of 9973 is slightly less than 100 (specifically, around 99.86). This means we only need to check for divisibility by prime numbers up to 97.

The prime numbers to check are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

Step 2: Check for divisibility step by step.

•2: The number ends in 3, which is odd. Not divisible by 2.
•3: The sum of the digits is 9 + 9 + 7 + 3 = 28. Since 28 is not divisible by 3, neither is 9973.
•5: The number does not end in 0 or 5. Not divisible by 5.
•7: 9973 ÷ 7 = 1424 with a remainder of 5. Not divisible.
•11: The alternating sum of the digits (3 - 7 + 9 - 9) is -4, which is not a multiple of 11. Not divisible.
•13: 9973 ÷ 13 = 767 with a remainder of 2. Not divisible.
•17: 9973 ÷ 17 = 586 with a remainder of 11. Not divisible.
•19: 9973 ÷ 19 = 524 with a remainder of 17. Not divisible.
•23: 9973 ÷ 23 = 433 with a remainder of 14. Not divisible.
•29: 9973 ÷ 29 = 343 with a remainder of 26. Not divisible.
•31: 9973 ÷ 31 = 321 with a remainder of 22. Not divisible.
•37: 9973 ÷ 37 = 269 with a remainder of 20. Not divisible.
•41: 9973 ÷ 41 = 243 with a remainder of 10. Not divisible.
•43: 9973 ÷ 43 = 231 with a remainder of 40. Not divisible.
•47: 9973 ÷ 47 = 212 with a remainder of 9. Not divisible.
•53: 9973 ÷ 53 = 188 with a remainder of 9. Not divisible.
•59: 9973 ÷ 59 = 169 with a remainder of 2. Not divisible.
•61: 9973 ÷ 61 = 163 with a remainder of 30. Not divisible.
•67: 9973 ÷ 67 = 148 with a remainder of 57. Not divisible.
•71: 9973 ÷ 71 = 140 with a remainder of 33. Not divisible.
•73: 9973 ÷ 73 = 136 with a remainder of 45. Not divisible.
•79: 9973 ÷ 79 = 126 with a remainder of 19. Not divisible.
•83: 9973 ÷ 83 = 120 with a remainder of 13. Not divisible.
•89: 9973 ÷ 89 = 112 with a remainder of 5. Not divisible.
•97: 9973 ÷ 97 = 102 with a remainder of 79. Not divisible.

Since 9973 has no prime factors other than 1 and itself, it is a prime number (in fact, it is the largest four-digit prime number).

[Yes]

sha256 e7cee07aea80… · 24 tokens in · 3,647 out · 23.0 s · via Google · stopped on its own

Sep 30, the whole day Question 2, every day

Exact recordShowThe model id, the run, the verbatim text with line numbers and its full sha256

Model: google/gemini-3.1-pro-preview
pinned google/gemini-3.1-pro-preview-20260219; alias resolved to google/gemini-3.1-pro-preview-20260219 at 2026-09-30 09:00:07 UTC (matches the pin)
Date: 2026-09-30 · run 20260930T090007Z-45ce12 · scorer v1
Scored: answered · correct · format ok
Changes: Minor Reverted length anomaly: went back to its usual answer length on the question whether 9973 is prime
sha256: e7cee07aea809d574956f70f8193e38d199b7cc4215957dff8c37a16848cb472
Permalink: https://modeldrift.watch/r/2026-09-30/D2/google/gemini-3.1-pro-preview/

Scored: answered · correct · format ok
Received: 2026-09-30 09:01:03 UTC
Run: 20260930T090007Z-45ce12
Served by: Google · HTTP 200 · finish stop
Size: 2,437 characters · 3,647 tokens out incl. hidden reasoning · 23.0 s

Highlighted: the last [Yes]/[No] bracket, which is the scored answer (Yes).

To determine if 9973 is a prime number, we can check if it is divisible by any prime number up to its square root. 
**Step 1: Find the square root of 9973.**
The square root of 10,000 is 100. Therefore, the square root of 9973 is slightly less than 100 (specifically, around 99.86). This means we only need to check for divisibility by prime numbers up to 97. 
The prime numbers to check are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
**Step 2: Check for divisibility step by step.**
*   **2**: The number ends in 3, which is odd. Not divisible by 2.
*   **3**: The sum of the digits is 9 + 9 + 7 + 3 = 28. Since 28 is not divisible by 3, neither is 9973.
*   **5**: The number does not end in 0 or 5. Not divisible by 5.
*   **7**: 9973 ÷ 7 = 1424 with a remainder of 5. Not divisible.
*   **11**: The alternating sum of the digits (3 - 7 + 9 - 9) is -4, which is not a multiple of 11. Not divisible.
*   **13**: 9973 ÷ 13 = 767 with a remainder of 2. Not divisible.
*   **17**: 9973 ÷ 17 = 586 with a remainder of 11. Not divisible.
*   **19**: 9973 ÷ 19 = 524 with a remainder of 17. Not divisible.
*   **23**: 9973 ÷ 23 = 433 with a remainder of 14. Not divisible.
*   **29**: 9973 ÷ 29 = 343 with a remainder of 26. Not divisible.
*   **31**: 9973 ÷ 31 = 321 with a remainder of 22. Not divisible.
*   **37**: 9973 ÷ 37 = 269 with a remainder of 20. Not divisible.
*   **41**: 9973 ÷ 41 = 243 with a remainder of 10. Not divisible.
*   **43**: 9973 ÷ 43 = 231 with a remainder of 40. Not divisible.
*   **47**: 9973 ÷ 47 = 212 with a remainder of 9. Not divisible.
*   **53**: 9973 ÷ 53 = 188 with a remainder of 9. Not divisible.
*   **59**: 9973 ÷ 59 = 169 with a remainder of 2. Not divisible.
*   **61**: 9973 ÷ 61 = 163 with a remainder of 30. Not divisible.
*   **67**: 9973 ÷ 67 = 148 with a remainder of 57. Not divisible.
*   **71**: 9973 ÷ 71 = 140 with a remainder of 33. Not divisible.
*   **73**: 9973 ÷ 73 = 136 with a remainder of 45. Not divisible.
*   **79**: 9973 ÷ 79 = 126 with a remainder of 19. Not divisible.
*   **83**: 9973 ÷ 83 = 120 with a remainder of 13. Not divisible.
*   **89**: 9973 ÷ 89 = 112 with a remainder of 5. Not divisible.
*   **97**: 9973 ÷ 97 = 102 with a remainder of 79. Not divisible.
Since 9973 has no prime factors other than 1 and itself, it is a prime number (in fact, it is the largest four-digit prime number).
[Yes]

End of response · 37 lines · 2,437 characters · sha256 e7cee07aea809d574956f70f8193e38d199b7cc4215957dff8c37a16848cb472