What does 'there exists' mean with respect to the philosophy of mathematics?

I'm having a difficult time understanding the philosophies of mathematics but my understanding is that even though people can make mathematics statements 'there exists a prime number between 6 and 8; it's 7' and an equivalent in German or with other symbols, grammars etc. There is nevertheless an underlying truth between all of these where the idea that the statements represents is true. The phrase 'there exists' seems somewhat Platonist but I don't actually believe that numbers exist on some level of reality that's higher than our own in some sense. I do think however these truths are mind independent. I don't believe that numbers are merely constructs in our minds because I like I said before I think there is some sort of underlying truth about numbers that already existed for us to discover and make constructions of.