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Your LimeSurvey version: 5.5.2+230109
Own server or LimeSurvey hosting:
Survey theme/template:
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I'd like to ask you about the technical aspects of the software. If 3 000 respondents fill in the questionnaire at the same time, will the software work? I mean, if it starts to chop, slow down, etc., whether the system can handle it. 
Does anyone have any experience?
Thank you.

This question can't really be answered, because it depends on so many factors.

First of all, I highly doubt that you will really have 3.000 concurrent users, even if you send the invitations all at the same time.

However, it is good practice to spread out invitations over the day or possibly over several days. Also, a "soft launch" is always a good idea, where you send out a small number of invitations and wait until you get the first responses, just to check that everything is working well.

Now with regards to the 3000 respondents "filling the questionnaire at the same time":

If Limesurvey can handle this depends very much on your hosting environment (server used, internet connection of the server, SSD vs. HDD, RAM, etc.).

Also the length of the survey can have a huge impact. Because if the survey just takes 5 minutes, the number of respondents that are filling in the survey at the same time is usually lower than for a survey that takes 60min.

Also a survey with a lot of conditions, filters, expression scripts, etc. will be "heavier" on the load than very straight forward simple questionnaires.

I think the main issue are the session files, which are fairly big in Limesurvey.

But with the right a decent hardware and a good "invitation strategy", spreading out the sending of invitations over the day or various days, I don't see any issues.