Claims

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2025_12_01_tao_teravainen: Tao and Teräväinen prove that for some absolute C infinitely many n have at most Ck distinct prime factors in n plus k for every positive k, answering yes; the site's curator records the problem as resolved by this preprint.

2026_04_16_lau: Lau proves that for some absolute C infinitely many n have at most C log k prime factors in n plus k for every k at least 2, which after a shift of n answers the question yes; the site's curator credits the improvement.

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