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You do not understand floating point numbers. 2^53 is not the largest integer that can be represented accurately in 64-bit floats. *All* the integers *from zero to 2^53* can be represented, but *many more larger than that* can too. Just not all of them.
In fact *every possible floating-point number greater than 2^53* is in fact an integer, all the way up to 1797693134862315708145274237317043567980705[removed a bunch of digits]23168738177180919299881250404026184124858368, which is the largest possible value.
4611686018427387904 is one such interger larger than 2^53 which *can* be represented as a float64. 4611686018427388000 is *not*. That number cannot exist in Javascript 4611686018427387904 can. And yet you get the wrong answer when you toString it.
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