Gemini on Question 2, Sep 10

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 has any prime factors less than or equal to its square root.

The square root of 9973 is approximately 99.86. Therefore, we need to check for divisibility by all prime numbers up to 97:
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.

Let's test a few:

•2: It is not even (ends in 3).
•3: The sum of its digits is 9 + 9 + 7 + 3 = 28, which is not divisible by 3.
•5: It does not end in 0 or 5.
•7: 9973 ÷ 7 = 1424 with a remainder of 5.
•11: The alternating sum of its digits is 9 - 9 + 7 - 3 = 4, which is not divisible by 11.
•13: 9973 ÷ 13 = 767 with a remainder of 2.
•17: 9973 ÷ 17 = 586 with a remainder of 11.
•19: 9973 ÷ 19 = 524 with a remainder of 17.

If we continue to divide 9973 by the rest of the prime numbers up to 97 (23, 29, 31... 97), we will find that none of them divide evenly into 9973 (they all leave a remainder). Because it has no positive divisors other than 1 and itself, it is a prime number. (In fact, 9973 is the largest four-digit prime number).

[Yes]

sha256 a950780bad88… · 24 tokens in · 3,611 out · 21.0 s · via Google · stopped on its own

Sep 10, 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; no alias snapshot recorded that day
Date: 2026-09-10 · run 20260910T221001Z-bb5bd1 · scorer v1
Scored: answered · correct · format ok
sha256: a950780bad881ff0c2b93ca17fa283fb2ed956f56dc76e758c1a0e119cff6a0f
Permalink: https://modeldrift.watch/r/2026-09-10/D2/google/gemini-3.1-pro-preview/

Scored: answered · correct · format ok
Received: 2026-09-10 22:10:56 UTC
Run: 20260910T221001Z-bb5bd1
Served by: Google · HTTP 200 · finish stop
Size: 1,137 characters · 3,611 tokens out incl. hidden reasoning · 21.0 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 has any prime factors less than or equal to its square root. 
The square root of 9973 is approximately 99.86. Therefore, we need to check for divisibility by all prime numbers up to 97:
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.
Let's test a few:
- **2**: It is not even (ends in 3).
- **3**: The sum of its digits is 9 + 9 + 7 + 3 = 28, which is not divisible by 3.
- **5**: It does not end in 0 or 5.
- **7**: 9973 ÷ 7 = 1424 with a remainder of 5.
- **11**: The alternating sum of its digits is 9 - 9 + 7 - 3 = 4, which is not divisible by 11.
- **13**: 9973 ÷ 13 = 767 with a remainder of 2.
- **17**: 9973 ÷ 17 = 586 with a remainder of 11.
- **19**: 9973 ÷ 19 = 524 with a remainder of 17.
If we continue to divide 9973 by the rest of the prime numbers up to 97 (23, 29, 31... 97), we will find that none of them divide evenly into 9973 (they all leave a remainder). Because it has no positive divisors other than 1 and itself, it is a prime number. (In fact, 9973 is the largest four-digit prime number).
[Yes]

End of response · 18 lines · 1,137 characters · sha256 a950780bad881ff0c2b93ca17fa283fb2ed956f56dc76e758c1a0e119cff6a0f