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Is there a list of firms out here which tend to not respond to Mass Mails if they are not interested in doing a Screener/CB?

I've slowly received a trickle of rejections, but tons of dead silence from others. I'm hoping it's a "we want to see how OCI goes before we respond" which probably means i'm out of luck, but i'll still hold out hope.

Also, if you haven't heard anything - no screener, etc - is there a rational to reaching out after 3-4 weeks to express some continued interest in being interviewed? Maybe they haven't gotten down to sending out the reject email/letter, but I wonder if an email stirring the pot could at least land an interview.

anyone have experience with this?

the list of firms that don't send rejection letters is about 1/2 of all firms.
yes, following up with a "resume update" or something is often done after a few weeks.