ENAIH ENcyclopedia of AI Hallucinations

Founded by Rudra Jadhav and Warren Woolf

Hallucination Entries

2 entries

category: Math / Arithmetic clear filters
  • 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.