Korean Air (according to google translate)

A survey request from our recent flight:

대한항공과 함께 즐겁고 편안한 여행 하셨는지요?

고객님의 소중한 의견을 듣고자 설문조사를 실시하고 있습니다. 잠시만 시간을 내주시면 감사하겠습니다.

We hope you had a pleasant trip with Korean Air.

Please answer this short survey to share your valuable feedback with us.

邀请您参与简短的问卷调查，与我们分享您的宝贵意见。

サービス品質向上のためのアンケート調査を行っております。ご協力お願い申し上げます。

The Korean text (according to google translate, my emphasis added):

Did you have a pleasant and comfortable trip with Korean Air?

We are conducting a survey to hear your valuable opinions. Thank you for taking a moment.

The Chinese text (atgt,mea):

You are invited to participate in a short survey to share your valuable opinions with us.

The Japanese text (atgt,mea):

We are conducting a questionnaire survey to improve service quality. Thank you for your cooperation.

Perfect numbers: Lichtman's Theorem (Part 1)

This summer, we are working through Jared Lichtman's recent proof that the primes achieve the maximal Erdős sum over primitive subsets of the natural numbers.

Quanta Magazine had a very nice article describing the theorem (formerly a conjecture of Erdős) which is the inspiration for this project. The article is here.

I will be posting notes on our conversations. The most important thing to understand: this project is about the journey and not the destination. We may not (probably won't!) get all the way through the paper. Along the way, we will take plenty of detours and excursions.