2 added 343 characters in body
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Wolfram Language (Mathematica), 31 bytes

Nearest[Prime~Array~78499,#,1]&

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                              & (*pure function*)
        Prime~Array~78499       (*among the (ascending) first 78499 primes*)
                            1   (*select one*)
Nearest[                 ,#, ]  (*which is nearest to the argument*)

1000003 is the 78499th prime. Nearest prioritizes values which appear earlier in the list (which are lower).

Wolfram Language (Mathematica), 31 bytes

Nearest[Prime~Array~78499,#,1]&

Try it online!

1000003 is the 78499th prime.

Wolfram Language (Mathematica), 31 bytes

Nearest[Prime~Array~78499,#,1]&

Try it online!

                              & (*pure function*)
        Prime~Array~78499       (*among the (ascending) first 78499 primes*)
                            1   (*select one*)
Nearest[                 ,#, ]  (*which is nearest to the argument*)

1000003 is the 78499th prime. Nearest prioritizes values which appear earlier in the list (which are lower).

1
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Wolfram Language (Mathematica), 31 bytes

Nearest[Prime~Array~78499,#,1]&

Try it online!

1000003 is the 78499th prime.