Claude on Question 2, Sep 30

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

Checking 9973

Since √9973 ≈ 99.9, I only need to test prime divisors up to 99.

Small primes:

•2: 9973 is odd → no
•3: digit sum = 9+9+7+3 = 28, not divisible by 3 → no
•5: doesn't end in 0 or 5 → no
•7: 7 × 1424 = 9968, remainder 5 → no
•11: alternating sum = 3 − 7 + 9 − 9 = −4 → no
•13: 13 × 767 = 9971, remainder 2 → no

Continuing:

•17: 17 × 586 = 9962, r = 11
•19: 19 × 524 = 9956, r = 17
•23: 23 × 433 = 9959, r = 14
•29: 29 × 343 = 9947, r = 26
•31: 31 × 321 = 9951, r = 22
•37: 37 × 269 = 9953, r = 20
•41: 41 × 243 = 9963, r = 10
•43: 43 × 231 = 9933, r = 40
•47: 47 × 212 = 9964, r = 9
•53: 53 × 188 = 9964, r = 9
•59: 59 × 169 = 9971, r = 2
•61: 61 × 163 = 9943, r = 30
•67: 67 × 148 = 9916, r = 57
•71: 71 × 140 = 9940, r = 33
•73: 73 × 136 = 9928, r = 45
•79: 79 × 126 = 9954, r = 19
•83: 83 × 120 = 9960, r = 13
•89: 89 × 112 = 9968, r = 5
•97: 97 × 102 = 9894, r = 79

No prime ≤ 99 divides 9973, so it is prime (in fact, it's the largest four-digit prime).

[Yes]

sha256 7b8ed8597e54… · 39 tokens in · 1,309 out · 12.7 s · via Claude Platform on AWS · 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: anthropic/claude-opus-5
pinned anthropic/claude-opus-5-20260723; alias resolved to anthropic/claude-opus-5-20260723 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
sha256: 7b8ed8597e5473e2081a33af01211c1ef5555b7c2393563711c3539317f88dd8
Permalink: https://modeldrift.watch/r/2026-09-30/D2/anthropic/claude-opus-5/

Scored: answered · correct · format ok
Received: 2026-09-30 09:00:40 UTC
Run: 20260930T090007Z-45ce12
Served by: Claude Platform on AWS · HTTP 200 · finish stop
Size: 1,121 characters · 1,309 tokens out incl. hidden reasoning · 12.7 s

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

## Checking 9973
Since √9973 ≈ 99.9, I only need to test prime divisors up to 99.
**Small primes:**
- **2:** 9973 is odd → no
- **3:** digit sum = 9+9+7+3 = 28, not divisible by 3 → no
- **5:** doesn't end in 0 or 5 → no
- **7:** 7 × 1424 = 9968, remainder 5 → no
- **11:** alternating sum = 3 − 7 + 9 − 9 = −4 → no
- **13:** 13 × 767 = 9971, remainder 2 → no
**Continuing:**
- **17:** 17 × 586 = 9962, r = 11
- **19:** 19 × 524 = 9956, r = 17
- **23:** 23 × 433 = 9959, r = 14
- **29:** 29 × 343 = 9947, r = 26
- **31:** 31 × 321 = 9951, r = 22
- **37:** 37 × 269 = 9953, r = 20
- **41:** 41 × 243 = 9963, r = 10
- **43:** 43 × 231 = 9933, r = 40
- **47:** 47 × 212 = 9964, r = 9
- **53:** 53 × 188 = 9964, r = 9
- **59:** 59 × 169 = 9971, r = 2
- **61:** 61 × 163 = 9943, r = 30
- **67:** 67 × 148 = 9916, r = 57
- **71:** 71 × 140 = 9940, r = 33
- **73:** 73 × 136 = 9928, r = 45
- **79:** 79 × 126 = 9954, r = 19
- **83:** 83 × 120 = 9960, r = 13
- **89:** 89 × 112 = 9968, r = 5
- **97:** 97 × 102 = 9894, r = 79
No prime ≤ 99 divides 9973, so it is prime (in fact, it's the largest four-digit prime).
**[Yes]**

End of response · 36 lines · 1,121 characters · sha256 7b8ed8597e5473e2081a33af01211c1ef5555b7c2393563711c3539317f88dd8