MODELDRIFT.WATCH

Sep 30 · Day 21

MINOR · GEMINI · QUESTION 2

Gemini went back to its usual answer length on the question whether 9973 is prime.

Why it’s minor

The change lasted one day before the model went back.

The full answers

Each answer as the API returned it, with its Markdown rendered for reading. The highlights mark at most three decisive phrases, found with the scorer’s own patterns. Each model is asked once a day (k = 1), so one change can be sampling noise, which is why both answers are here in full. How scoring works.

Asked verbatim · Question 2, the one that is prime

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

SEP 29the changePermalink

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

  • 1.The square root of 9973 is approximately 99.86. So, we need to test prime numbers up to 99:

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.

  • 2.Let's do some quick checks for the smallest primes:
  • •2: 9973 is not even.
  • •3: The sum of the digits (9 + 9 + 7 + 3 = 28) 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 digits (3 - 7 + 9 - 9 = -4) is not a multiple of 11.
  • 3.We can continue this division for the rest of the primes up to 97:
  • •9973 / 13 = 767 remainder 2
  • •9973 / 17 = 586 remainder 11
  • •9973 / 19 = 524 remainder 17
  • •...
  • •9973 / 89 = 112 remainder 5
  • •9973 / 97 = 102 remainder 79

Since 9973 cannot be evenly divided by any prime number up to its square root, it has no divisors other than 1 and itself. (In fact, 9973 is well-known in mathematics for being the largest four-digit prime number).

[Yes]

SEP 30backPermalink

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]

Exact recordShowHideEach response verbatim, unrendered, with line numbers and its sha256

Deviation the day it changed

2026-09-29 permalink

Scored
answered · correct · format ok
Received
2026-09-29 09:00:56 UTC
Run
20260929T090007Z-334891
Served by
Google · HTTP 200 · finish stop
Size
1,094 characters · 2,715 tokens out incl. hidden reasoning · 18.0 s
To determine if 9973 is a prime number, we can check if it is divisible by any prime numbers up to its square root.
1. The square root of 9973 is approximately 99.86. So, we need to test prime numbers up to 99:
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.
2. Let's do some quick checks for the smallest primes:
- **2**: 9973 is not even.
- **3**: The sum of the digits (9 + 9 + 7 + 3 = 28) 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 digits (3 - 7 + 9 - 9 = -4) is not a multiple of 11.
3. We can continue this division for the rest of the primes up to 97:
- 9973 / 13 = 767 remainder 2
- 9973 / 17 = 586 remainder 11
- 9973 / 19 = 524 remainder 17
- ...
- 9973 / 89 = 112 remainder 5
- 9973 / 97 = 102 remainder 79
Since 9973 cannot be evenly divided by any prime number up to its square root, it has no divisors other than 1 and itself. (In fact, 9973 is well-known in mathematics for being the largest four-digit prime number).
[Yes]

End of response · 23 lines · 1,094 characters · sha256 57b3463110bd01e340cedfa506e4e303adb592604b176b1f757e707533c8fa3c

Reverted back to baseline

2026-09-30 permalink

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
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

Record detailsShowHideModel version, runs, baseline, triage, permalink, event ID
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)
Prompt
Question 2: D2 (drift)
Why this question
9973 really is prime, which catches a model that has simply learned to say no.
Scored
format ok if the response ends with a [Yes]/[No] bracket
Change
460 → 274
Baseline
6 prior days with data; 7 matched the baseline value (2026-09-22, 2026-09-23, 2026-09-25, 2026-09-26, 2026-09-27, 2026-09-28, 2026-09-29)
Responses
deviation 2026-09-29 09:00:56 UTC, run 20260929T090007Z-334891; reverted 2026-09-30 09:01:03 UTC, run 20260930T090007Z-45ce12
Detected
2026-09-30 · run 20260930T090007Z-45ce12, started 2026-09-30 09:00:07 UTC · scorer v1 · severity rules r2
Permalink
https://modeldrift.watch/e/2026-09-30/D2/google/gemini-3.1-pro-preview/transient_anomaly/length_tokens/
Event ID
2026-09-30:D2:google/gemini-3.1-pro-preview:transient_anomaly:length_tokens

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