Shortest "arithmetic" formula to output 1000 primes
Score 1164 883 835 772 601 574 554 506
541^n*743^(n/2)*(-1)^(n/4)*17^(n/8)%2310+297999352693782350435634574256421873511169209139789986107407037031463672744907435566931682004950168827622126589004268258979810886896053712313147567393521260370898856430728936238509646240927399434529133911694916958518274696252190810912239170743768597920487389824644988723446125401158124982957878348425345764310640796665180984553241724855646631162669954988652785474199384658696484753453854147610893664426900411229033105555630617039087023847065224114331551958/67^(n%250)%67*2310

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(OP hasn’t answered my question about the behavior of / and % on negative numbers, so this answer works under the floored or Euclidean conventions where (-1) % 2310 = 2309.)