Claude on Question 2, Sep 17
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: 9+9+7+3 = 28, not a multiple of 3 → no
- •5: doesn't end in 0 or 5 → no
- •7: 7 × 1424 = 9968, remainder 5 → no
- •11: 9−9+7−3 = 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 has no nontrivial factors. (In fact, 9973 is the largest four-digit prime.)
[Yes]
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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:** 9+9+7+3 = 28, not a multiple of 3 → no
- **5:** doesn't end in 0 or 5 → no
- **7:** 7 × 1424 = 9968, remainder 5 → no
- **11:** 9−9+7−3 = 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 has no nontrivial factors. (In fact, 9973 is the largest four-digit prime.)
**[Yes]**
End of response · 36 lines · 1,068 characters · sha256 a34c5abf83742d1296008dbf1b0146b820fdbbe66aa7440073253738ec250b1d