Gemini gave a shorter answer than usual to the question whether 9973 is prime, about 60% of its usual length.
GeminiSep 28
Is 9973 a prime number? Think step by step and then answer "[Yes]" or "[No]".302 wordsin its answer. From Sep 22 to 28 its answers ran between 264 and 400 words.
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.Find the square root: The square root of 9973 is approximately 99.86. Therefore, we only…
GeminiSep 29
Is 9973 a prime number? Think step by step and then answer "[Yes]" or "[No]".214 wordsin its answer, about 60% of its usual length.
To determine if 9973 is a prime number, we can check if it is divisible by any prime numbers up to its square root.The square root of 9973 is approximately 99.86. So, we need to test prime numbers up to 99:…
Why it’s minor
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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
SEP 28beforePermalink
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.
- 1.Find the square root: The square root of 9973 is approximately 99.86. Therefore, we only need to test for divisibility by prime numbers up to 97.
- 2.Check small primes:
- •2: The number 9973 ends in 3 (an odd number), so it is not divisible by 2.
- •3: The sum of its digits is 9 + 9 + 7 + 3 = 28. Since 28 is not divisible by 3, 9973 is not divisible by 3.
- •5: The number does not end in 0 or 5, so it is not divisible by 5.
- 3.Check larger primes (up to 97):
- •7: 9973 ÷ 7 = 1424 remainder 5.
- •11: The alternating sum of its digits is 9 - 9 + 7 - 3 = 4, which is not divisible by 11.
- •13: 9973 ÷ 13 = 767 remainder 2.
- •17: 9973 ÷ 17 = 586 remainder 11.
- •19: 9973 ÷ 19 = 524 remainder 17.
- •23: 9973 ÷ 23 = 433 remainder 14.
- •29: 9973 ÷ 29 = 343 remainder 26.
- •31: 9973 ÷ 31 = 321 remainder 22.
- •37: 9973 ÷ 37 = 269 remainder 20.
- •41: 9973 ÷ 41 = 243 remainder 10.
- •43: 9973 ÷ 43 = 231 remainder 40.
- •47: 9973 ÷ 47 = 212 remainder 9.
- •53: 9973 ÷ 53 = 188 remainder 9.
- •59: 9973 ÷ 59 = 169 remainder 2.
- •61: 9973 ÷ 61 = 163 remainder 30.
- •67: 9973 ÷ 67 = 148 remainder 57.
- •71: 9973 ÷ 71 = 140 remainder 33.
- •73: 9973 ÷ 73 = 136 remainder 45.
- •79: 9973 ÷ 79 = 126 remainder 19.
- •83: 9973 ÷ 83 = 120 remainder 13.
- •89: 9973 ÷ 89 = 112 remainder 5.
- •97: 9973 ÷ 97 = 102 remainder 79.
Since 9973 cannot be evenly divided by any prime number up to its square root, it has no positive divisors other than 1 and itself. (In fact, 9973 is the largest four-digit prime number).
[Yes]
SEP 29afterPermalink
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]
Exact recordShowHideEach response verbatim, unrendered, with line numbers and its sha256
Before baseline
2026-09-28 permalink
- Scored
- answered · correct · format ok
- Received
- 2026-09-28 09:01:00 UTC
- Run
- 20260928T090007Z-07d4be
- Served by
- Google · HTTP 200 · finish stop
- Size
- 1,809 characters · 3,387 tokens out incl. hidden reasoning · 20.7 s
End of response · 34 lines · 1,809 characters · sha256 857a9eb65da19d495d5e1fc92137f5454b806020879432fa8a5e0fdf560edb4d
After this run
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
End of response · 23 lines · 1,094 characters · sha256 57b3463110bd01e340cedfa506e4e303adb592604b176b1f757e707533c8fa3c
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