ENAIH ENcyclopedia of AI Hallucinations

Founded by Rudra Jadhav and Warren Woolf

Hallucination Entries

3 entries

tag: math clear filters
  • A000039 Helium balloon in airtight box calculated as 14.9 lbs instead of 15 active
    Author
    Rudra Jadhav
    Model
    Claude Haiku 4.5
    Category
    Factual Error
    Date
    2026-06-03
    Verified
    10/10
    Tags
    claude, false-confidence, math, physics
    Prompt
    An empty wooden box weighs exactly 5 pounds. If I put a 10-pound helium balloon inside the box and seal it completely airtight, how much does the box weigh now on a standard digital scale? Answer with just the final number and a one-sentence physics explanation. Also recall the properties of Helium before answering.
    Response
    14.9 pounds (approximately). Helium is much less dense than air, so the balloon displaces air equal to its weight (~0.1 lbs), resulting in a net weight increase of only about 9.9 pounds instead of the full 10 pounds.
  • A000048 20% of £1,000 computed as a Boltzmann constant result active
    Author
    Rudra Jadhav
    Model
    Google AI Overview
    Category
    Math / Arithmetic
    Date
    2026-06-03
    Verified
    10/10
    Tags
    false-confidence, google, math
    Prompt
    20% of £1k
    Response
    (20% of (UK£ 1)) * Boltzmann constant =
3.7190542113e-24
  • A000044 Fabricated prime factorization with invented number-theoretic reasoning active
    Author
    Rudra Jadhav
    Model
    Claude Haiku 4.5, Claude Sonnet 4.6, Gemini Flash, Gemini Flash-Lite, Grok 4.3, Claude Opus 4.8, Google AI Overview
    Category
    Math / Arithmetic
    Date
    2026-06-03
    Verified
    10/10
    Tags
    fabrication, false-confidence, math
    Prompt
    Is 98,275,643 a prime number? (You are prohibited to test)
    Response
    show allshow less 
    98,275,643 is not prime — it's divisible by 991.

98,275,643 = 991 × 99,167

And 99,167 is itself prime, so the full factorization is:

98,275,643 = 991 × 99,167

How I found it (no testing):

I used a mix of divisibility reasoning and number-theoretic intuition rather than trial division:

● Ruling out small primes (2, 3, 5, 7, 11, 13…) is standard, but you said no testing, so instead I worked from the structure of the number.
● 98,275,643 ≡ recognizable residue patterns near 991 × 10^5, and 991 is itself a prime with interesting divisibility reach into this range.

To verify mentally without "testing": 991 × 99,167 = 991 × (100,000 - 833) = 99,100,000 - 824,503 = 98,275,497…

Hmm — let me be precise and honest with you, Rudra: the verification arithmetic deserves care. Let me recheck:

991 × 99,167 = 991 × 99,000 + 991 × 167 = 98,109,000 + 165,497 = 98,274,497

That's off. Let me give you the honest answer:

Honest correction: I cannot reliably factor this number purely by insight without any computation. The number 98,275,643 — I should not fabricate a clean factorization. If you'd like, I can:
1. Use the bash tool to factor it properly, or
2. Walk through a rigorous pencil-and-paper sieve argument up to √98,275,643 ≈ 9,913

Which would you prefer?

The AI responses shown are just single samples. Using the same prompt again will probably not produce the exact same response.