Gemini on Question 2, Oct 1

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

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

The square root of 9973 is approximately 99.86 (since 100² = 10000). Therefore, we need to test 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 them:

•2: It is an odd number, so it is not divisible by 2.
•3: The sum of its digits (9 + 9 + 7 + 3 = 28) is not divisible by 3.
•5: It does not end in 0 or 5.
•7: 9973 = 7 × 1424 + 5 (not divisible)
•11: The alternating sum of digits (9 - 9 + 7 - 3 = 4) is not divisible by 11.
•13: 9973 = 13 × 767 + 2 (not divisible)
•17: 9973 = 17 × 586 + 11 (not divisible)
•19: 9973 = 19 × 524 + 17 (not divisible)
•23: 9973 = 23 × 433 + 14 (not divisible)
•29: 9973 = 29 × 343 + 26 (not divisible)
•31: 9973 = 31 × 321 + 22 (not divisible)
•37: 9973 = 37 × 269 + 20 (not divisible)
•41: 9973 = 41 × 243 + 10 (not divisible)
•43: 9973 = 43 × 231 + 40 (not divisible)
•47: 9973 = 47 × 212 + 9 (not divisible)
•53: 9973 = 53 × 188 + 9 (not divisible)
•59: 9973 = 59 × 169 + 2 (not divisible)
•61: 9973 = 61 × 163 + 30 (not divisible)
•67: 9973 = 67 × 148 + 57 (not divisible)
•71: 9973 = 71 × 140 + 33 (not divisible)
•73: 9973 = 73 × 136 + 45 (not divisible)
•79: 9973 = 79 × 126 + 19 (not divisible)
•83: 9973 = 83 × 120 + 13 (not divisible)
•89: 9973 = 89 × 112 + 5 (not divisible)
•97: 9973 = 97 × 102 + 79 (not divisible)

Since 9973 is not divisible by any prime number up to its square root, it only has exactly two distinct positive divisors: 1 and itself. (In fact, 9973 holds the title for being the largest four-digit prime number).

[Yes]

sha256 ddc718c029ec… · 24 tokens in · 4,368 out · 28.1 s · via Google · stopped on its own

Oct 1, 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 2026-10-01 09:00:06 UTC (matches the pin)
Date: 2026-10-01 · run 20261001T090007Z-857bc9 · scorer v1
Scored: answered · correct · format ok
sha256: ddc718c029ec67330dcb58bc9eee1c6d07df29e57d50d168d372608668576e17
Permalink: https://modeldrift.watch/r/2026-10-01/D2/google/gemini-3.1-pro-preview/

Scored: answered · correct · format ok
Received: 2026-10-01 09:01:06 UTC
Run: 20261001T090007Z-857bc9
Served by: Google · HTTP 200 · finish stop
Size: 1,842 characters · 4,368 tokens out incl. hidden reasoning · 28.1 s

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

To determine if 9973 is a prime number, we need to check if it is divisible by any prime numbers up to its square root. 
The square root of 9973 is approximately 99.86 (since 100² = 10000). Therefore, we need to test 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 them:
- **2**: It is an odd number, so it is not divisible by 2.
- **3**: The sum of its digits (9 + 9 + 7 + 3 = 28) is not divisible by 3.
- **5**: It does not end in 0 or 5.
- **7**: 9973 = 7 × 1424 + 5 (not divisible)
- **11**: The alternating sum of digits (9 - 9 + 7 - 3 = 4) is not divisible by 11.
- **13**: 9973 = 13 × 767 + 2 (not divisible)
- **17**: 9973 = 17 × 586 + 11 (not divisible)
- **19**: 9973 = 19 × 524 + 17 (not divisible)
- **23**: 9973 = 23 × 433 + 14 (not divisible)
- **29**: 9973 = 29 × 343 + 26 (not divisible)
- **31**: 9973 = 31 × 321 + 22 (not divisible)
- **37**: 9973 = 37 × 269 + 20 (not divisible)
- **41**: 9973 = 41 × 243 + 10 (not divisible)
- **43**: 9973 = 43 × 231 + 40 (not divisible)
- **47**: 9973 = 47 × 212 + 9 (not divisible)
- **53**: 9973 = 53 × 188 + 9 (not divisible)
- **59**: 9973 = 59 × 169 + 2 (not divisible)
- **61**: 9973 = 61 × 163 + 30 (not divisible)
- **67**: 9973 = 67 × 148 + 57 (not divisible)
- **71**: 9973 = 71 × 140 + 33 (not divisible)
- **73**: 9973 = 73 × 136 + 45 (not divisible)
- **79**: 9973 = 79 × 126 + 19 (not divisible)
- **83**: 9973 = 83 × 120 + 13 (not divisible)
- **89**: 9973 = 89 × 112 + 5 (not divisible)
- **97**: 9973 = 97 × 102 + 79 (not divisible)
Since 9973 is not divisible by any prime number up to its square root, it only has exactly two distinct positive divisors: 1 and itself. (In fact, 9973 holds the title for being the largest four-digit prime number).
[Yes]

End of response · 35 lines · 1,842 characters · sha256 ddc718c029ec67330dcb58bc9eee1c6d07df29e57d50d168d372608668576e17