Last Updated
：2025/12/07
Dickson's conjecture
Proper noun
Japanese Meaning
（数論）ディクソン予想。具体的には、各bᵢが1以上である有限個の一次式 a₁ + b₁n, a₂ + b₂n, …, aₖ + bₖn において、特定の合同条件によって成立が妨げられない場合、これらすべてが素数となる正の整数 n が無限に存在するという予想。
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(number theory) The conjecture that, for a finite set of linear forms a₁ + b₁n, a₂ + b₂n, ..., aₖ + bₖn with bᵢ ≥ 1, there are infinitely many positive integers n for which they are all prime, unless there is a congruence condition preventing this.
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Dickson's conjecture
Although unproven, Dickson's conjecture has motivated extensive research into when several linear forms a₁ + b₁n, a₂ + b₂n, ..., a_k + b_kn can all be prime simultaneously.
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Although unproven, Dickson's conjecture has motivated extensive research into when several linear forms a₁ + b₁n, a₂ + b₂n, ..., a_k + b_kn can all be prime simultaneously.
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