An amateur using ChatGPT solves an Erdős problem

A solution produced by GPT-5.4 Pro drew attention in the long-standing problem of the minimum value of the Erdős sum for primitive sets.

• Liam Price posted a proof obtained from a single prompt to ChatGPT on erdosproblems.com, which was then reviewed by Kevin Barreto and other experts.
• The problem concerns primitive sets, in which no element of the set divides another, and relates to the conjecture that the minimum value of the Erdős sum is 1, approaching that value as the elements grow larger.
• This proof did not follow the path people usually think of first, but instead combined known formulas from related fields in an unexpected way; the original proof was rough, but experts refined the core idea into a shorter form.
• Terence Tao noted that the problem might have been easier than expected, and that there may have been a mental block regarding existing approaches.
• There have been previous cases of AI solving several Erdős problems, but this case caused a bigger stir in terms of difficulty and novelty.