Andrica's conjecture, named after Romanian mathematician Dorin Andrica who proposed it in 1986, is a conjecture about the gaps between consecutive prime numbers, bounding how quickly the square roots of successive primes can grow apart. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementFor the n-th prime p_n, the inequality sqrt(p_(n+1)) - sqrt(p_n) < 1 holds for all n; equivalently the n-th prime gap g_n is less than 2 sqrt(p_n) + 1. 1 Proposed Year Progress Toward ResolutionUnproven. Imran Ghory used data on the largest prime gaps to confirm the conjecture for n up to 1.3002 x 10^16, and a more recent table of maximal gaps extends the confirmation exhaustively to 2 x 10^19, beyond 2^64. 1 Classification
Resolution Status Prize Status
Prize Status (category) Sources
1. Andrica's Conjecture (Wikipedia)
Wikimedia FoundationLead section
Andrica, D. (1986). Note on a conjecture in prime number theory
Lead section, second sentence
The conjecture states that the inequality
Empirical evidence section
Imran Ghory has used data on the largest prime gaps to confirm the conjecture for n up to
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