Theta certificate data, block 0

Definition
ThetaCertData_0
by @bwdaugherty · Oct 16, 2026 · Mathlib 0df444a (Lean v4.33.1)
analytic-number-theorynumber-theoryprime-numbers
Certificate records, block 0 of 102, for $|\theta(t)-t|\le t/(5\log^2 t)$ on $[3594641, 3584912847]$ : each record is a segment of odd numbers, its split into windows, and fixed-point bounds for $Q\,\theta$ at its two ends ( $Q=2^{64}$ ).
The data are produced by a program and are checked, not trusted: the theorem ThetaCert.run_0 states that the kernel checker accepts every record.
Retired (2026-10-17) Superseded: this mesh block is not used, because the full mesh of the Chebyshev certificate exceeds the platform's per-job memory and time limits. The full Chebyshev certificate and its proof Dusart.chebyshev_theta_k2_finite are in the release doi:10.5281/zenodo.23432990; the checker and base range on this platform remain ThetaCertCore, ThetaCertData_base and ThetaCert.base.
Definition code
import Definitions.Def_ThetaCertCore

namespace ThetaSieve
set_option maxRecDepth 100000

def ThetaRun0.s0 : Seg := ⟨66251107453349134926774791, 66251107453349136183101682, 3594641, 775844, [4, 8, 7, 8, 7, 15, 31, 30, 15, 23, 30, 30, 30, 61, 68, 60, 68, 45, 61, 37, 46, 45, 30, 38, 53, 53, 75, 53, 68, 53, 53, 53, 53, 98, 113, 136, 121, 106, 121, 113, 121, 136, 136, 136, 121, 98, 83, 128, 159, 181, 174, 166, 159, 151, 159, 166, 143, 121, 106, 143, 136, 144, 151, 196, 152, 196, 166, 182, 204, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 214, 205, 222, 222, 191, 151, 166, 159, 144, 181, 219, 220, 223, 223, 223, 223, 223, 223, 223, 223, 220, 223, 193, 196, 182, 159, 181, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 217, 196, 189, 223, 223, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 246, 246, 246, 246, 246, 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258, 258, 258, 258, 258, 258, 258, 258, 258, 258, 258, 258, 258, 258, 258, 258, 258, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 259, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 260, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 261, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 263, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 264, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 265, 266, 266, 266, 266, 263, 244, 237, 245, 245, 266, 266, 266, 266, 266, 266, 240, 230, 266, 246, 199, 266, 266, 266, 243, 221, 230, 260, 214, 266, 266, 266, 266, 266, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 267, 268, 268, 268, 268, 268, 268, 268, 268, 255, 260, 245, 268, 268, 222, 268, 237, 214, 222, 230, 230, 199, 199, 191, 214, 230, 260, 253, 229, 230, 268, 268, 207, 222, 214, 222, 168, 153, 146, 161, 145, 138, 138, 138, 160, 169, 191, 161, 207, 168, 168, 169, 199, 245, 269, 269, 243, 260, 260, 253, 253, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 269, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 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277, 277, 277, 277, 277, 277, 277, 277, 277, 277, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 278, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 279, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 280, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 281, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 282, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 283, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 284, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 285, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 286, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 287, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 289, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 290, 291, 291, 291, 291, 291, 291, 291, 291, 291, 291, 291, 291, 291, 291, 291, 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313, 313, 313, 313, 313, 313, 313, 313, 313, 313, 314, 314], 94900393007475333079113450, 94900619677773581487276132⟩
def ThetaRun0.s1 : Seg := ⟨94900393007475333079113450, 94900619677773581487276132, 5146329, 1048576, [314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 314, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 315, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 316, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 317, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 318, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 319, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 320, 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def ThetaRun0.s2 : Seg := ⟨133573964074755540505892336, 133574492265183916893103076, 7243481, 1048576, [442, 442, 442, 442, 442, 442, 442, 442, 442, 442, 442, 442, 442, 442, 442, 442, 442, 443, 443, 443, 443, 443, 443, 443, 443, 443, 443, 443, 443, 443, 443, 443, 443, 443, 443, 443, 444, 444, 444, 444, 444, 444, 444, 444, 444, 444, 444, 444, 444, 444, 444, 444, 444, 444, 445, 445, 445, 445, 445, 445, 445, 445, 445, 445, 445, 445, 445, 445, 445, 445, 445, 445, 446, 446, 446, 446, 446, 446, 446, 446, 446, 446, 446, 446, 446, 446, 446, 446, 446, 446, 446, 447, 447, 447, 447, 447, 447, 447, 447, 447, 447, 447, 447, 447, 447, 447, 447, 447, 447, 448, 448, 448, 448, 448, 448, 448, 448, 448, 448, 448, 448, 448, 448, 448, 448, 448, 448, 449, 449, 449, 449, 449, 449, 449, 449, 449, 449, 449, 449, 449, 449, 449, 449, 449, 449, 449, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 451, 451, 451, 451, 451, 451, 451, 451, 451, 451, 451, 451, 451, 451, 451, 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def ThetaRun0.s3 : Seg := ⟨172247703964792000000304702, 172248528221267816054546971, 9340633, 1048576, [570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 571, 571, 571, 571, 571, 571, 571, 571, 571, 571, 571, 571, 571, 571, 571, 572, 572, 572, 572, 572, 572, 572, 572, 572, 572, 572, 572, 572, 572, 573, 573, 573, 573, 573, 573, 573, 573, 573, 573, 573, 573, 573, 573, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 575, 575, 575, 575, 575, 575, 575, 575, 575, 575, 575, 575, 575, 575, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 577, 577, 577, 577, 577, 577, 577, 577, 577, 577, 577, 577, 577, 577, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 579, 579, 579, 579, 579, 579, 579, 579, 579, 579, 579, 579, 579, 579, 579, 580, 580, 580, 580, 580, 580, 580, 580, 580, 580, 580, 580, 580, 580, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 582, 582, 582, 582, 582, 582, 582, 582, 582, 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def ThetaRun0.s4 : Seg := ⟨210907404752430730168935478, 210908520856852815603742516, 11437785, 1048576, [698, 698, 698, 698, 698, 698, 698, 698, 698, 698, 698, 699, 699, 699, 699, 699, 699, 699, 699, 699, 699, 699, 699, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 701, 701, 701, 701, 701, 701, 701, 701, 701, 701, 701, 701, 702, 702, 702, 702, 702, 702, 702, 702, 702, 702, 702, 702, 703, 703, 703, 703, 703, 703, 703, 703, 703, 703, 703, 704, 704, 704, 704, 704, 704, 704, 704, 704, 704, 704, 704, 705, 705, 705, 705, 705, 705, 705, 705, 705, 705, 705, 705, 706, 706, 706, 706, 706, 706, 706, 706, 706, 706, 706, 707, 707, 707, 707, 707, 707, 707, 707, 707, 707, 707, 707, 708, 708, 708, 708, 708, 708, 708, 708, 708, 708, 708, 709, 709, 709, 709, 709, 709, 709, 709, 709, 709, 709, 709, 710, 710, 710, 710, 710, 710, 710, 710, 710, 710, 710, 710, 711, 711, 711, 711, 711, 711, 711, 711, 711, 711, 711, 712, 712, 712, 712, 712, 712, 712, 712, 712, 712, 712, 712, 713, 713, 713, 713, 713, 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825, 107], 249583001885138119751250177, 249584406716624359460198012⟩
def ThetaRun0.s5 : Seg := ⟨249583001885138119751250177, 249584406716624359460198012, 13534937, 1048576, [826, 826, 826, 826, 826, 826, 826, 826, 826, 827, 827, 827, 827, 827, 827, 827, 827, 827, 827, 828, 828, 828, 828, 828, 828, 828, 828, 828, 828, 829, 829, 829, 829, 829, 829, 829, 829, 829, 829, 830, 830, 830, 830, 830, 830, 830, 830, 830, 830, 831, 831, 831, 831, 831, 831, 831, 831, 831, 831, 832, 832, 832, 832, 832, 832, 832, 832, 832, 832, 833, 833, 833, 833, 833, 833, 833, 833, 833, 834, 834, 834, 834, 834, 834, 834, 834, 834, 834, 835, 835, 835, 835, 835, 835, 835, 835, 835, 835, 836, 836, 836, 836, 836, 836, 836, 836, 836, 836, 837, 837, 837, 837, 837, 837, 837, 837, 837, 837, 838, 838, 838, 838, 838, 838, 838, 838, 838, 839, 839, 839, 839, 839, 839, 839, 839, 839, 839, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 841, 841, 841, 841, 841, 841, 841, 841, 841, 841, 842, 842, 842, 842, 842, 842, 842, 842, 842, 843, 843, 843, 843, 843, 843, 843, 843, 843, 843, 844, 844, 844, 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953, 766], 288275117781901831773521441, 288276808744050798596170879⟩
def ThetaRun0.s6 : Seg := ⟨288275117781901831773521441, 288276808744050798596170879, 15632089, 1048576, [954, 954, 954, 954, 954, 954, 954, 954, 955, 955, 955, 955, 955, 955, 955, 955, 955, 956, 956, 956, 956, 956, 956, 956, 956, 957, 957, 957, 957, 957, 957, 957, 957, 957, 958, 958, 958, 958, 958, 958, 958, 958, 959, 959, 959, 959, 959, 959, 959, 959, 959, 960, 960, 960, 960, 960, 960, 960, 960, 960, 961, 961, 961, 961, 961, 961, 961, 961, 962, 962, 962, 962, 962, 962, 962, 962, 962, 963, 963, 963, 963, 963, 963, 963, 963, 964, 964, 964, 964, 964, 964, 964, 964, 964, 965, 965, 965, 965, 965, 965, 965, 965, 966, 966, 966, 966, 966, 966, 966, 966, 966, 967, 967, 967, 967, 967, 967, 967, 967, 968, 968, 968, 968, 968, 968, 968, 968, 969, 969, 969, 969, 969, 969, 969, 969, 969, 970, 970, 970, 970, 970, 970, 970, 970, 971, 971, 971, 971, 971, 971, 971, 971, 971, 972, 972, 972, 972, 972, 972, 972, 972, 973, 973, 973, 973, 973, 973, 973, 973, 973, 974, 974, 974, 974, 974, 974, 974, 974, 975, 975, 975, 975, 975, 975, 975, 975, 976, 976, 976, 976, 976, 976, 976, 976, 976, 977, 977, 977, 977, 977, 977, 977, 977, 978, 978, 978, 978, 978, 978, 978, 978, 978, 979, 979, 979, 979, 979, 979, 979, 979, 980, 980, 980, 980, 980, 980, 980, 980, 981, 981, 981, 981, 981, 981, 981, 981, 981, 982, 982, 982, 982, 982, 982, 982, 982, 983, 983, 983, 983, 983, 983, 983, 983, 984, 984, 984, 984, 984, 984, 984, 984, 984, 985, 985, 985, 985, 985, 985, 985, 985, 986, 986, 986, 986, 986, 986, 986, 986, 987, 987, 987, 987, 987, 987, 987, 987, 987, 988, 988, 988, 988, 988, 988, 988, 988, 989, 989, 989, 989, 989, 989, 989, 989, 990, 990, 990, 990, 990, 990, 990, 990, 991, 991, 991, 991, 991, 991, 991, 991, 991, 992, 992, 992, 992, 992, 992, 992, 992, 993, 993, 993, 993, 993, 993, 993, 993, 994, 994, 994, 994, 994, 994, 994, 994, 995, 995, 995, 995, 995, 995, 995, 995, 995, 996, 996, 996, 996, 996, 996, 996, 996, 997, 997, 997, 997, 997, 997, 997, 997, 998, 998, 998, 998, 998, 998, 998, 998, 999, 999, 999, 999, 999, 999, 999, 999, 999, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1001, 1001, 1001, 1001, 1001, 1001, 1001, 1001, 1002, 1002, 1002, 1002, 1002, 1002, 1002, 1002, 1003, 1003, 1003, 1003, 1003, 1003, 1003, 1003, 1004, 1004, 1004, 1004, 1004, 1004, 1004, 1004, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1006, 1006, 1006, 1006, 1006, 1006, 1006, 1006, 1007, 1007, 1007, 1007, 1007, 1007, 1007, 1007, 1008, 1008, 1008, 1008, 1008, 1008, 1008, 1008, 1009, 1009, 1009, 1009, 1009, 1009, 1009, 1009, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1011, 1011, 1011, 1011, 1011, 1011, 1011, 1011, 1012, 1012, 1012, 1012, 1012, 1012, 1012, 1012, 1013, 1013, 1013, 1013, 1013, 1013, 1013, 1013, 1013, 1014, 1014, 1014, 1014, 1014, 1014, 1014, 1014, 1015, 1015, 1015, 1015, 1015, 1015, 1015, 1015, 1016, 1016, 1016, 1016, 1016, 1016, 1016, 1016, 1017, 1017, 1017, 1017, 1017, 1017, 1017, 1017, 1018, 1018, 1018, 1018, 1018, 1018, 1018, 1018, 1019, 1019, 1019, 1019, 1019, 1019, 1019, 1019, 1020, 1020, 1020, 1020, 1020, 1020, 1020, 1020, 1021, 1021, 1021, 1021, 1021, 1021, 1021, 1021, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1023, 1023, 1023, 1023, 1023, 1023, 1023, 1023, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1025, 1025, 1025, 1025, 1025, 1025, 1025, 1025, 1026, 1026, 1026, 1026, 1026, 1026, 1026, 1026, 1027, 1027, 1027, 1027, 1027, 1027, 1027, 1027, 1028, 1028, 1028, 1028, 1028, 1028, 1028, 1028, 1029, 1029, 1029, 1029, 1029, 1029, 1029, 1029, 1030, 1030, 1030, 1030, 1030, 1030, 1030, 1030, 1031, 1031, 1031, 1031, 1031, 1031, 1031, 1031, 1032, 1032, 1032, 1032, 1032, 1032, 1032, 1032, 1033, 1033, 1033, 1033, 1033, 1033, 1033, 1033, 1034, 1034, 1034, 1034, 1034, 1034, 1034, 1034, 1035, 1035, 1035, 1035, 1035, 1035, 1035, 1036, 1036, 1036, 1036, 1036, 1036, 1036, 1036, 1037, 1037, 1037, 1037, 1037, 1037, 1037, 1037, 1038, 1038, 1038, 1038, 1038, 1038, 1038, 1038, 1039, 1039, 1039, 1039, 1039, 1039, 1039, 1039, 1040, 1040, 1040, 1040, 1040, 1040, 1040, 1040, 1041, 1041, 1041, 1041, 1041, 1041, 1041, 1041, 1042, 1042, 1042, 1042, 1042, 1042, 1042, 1042, 1043, 1043, 1043, 1043, 1043, 1043, 1043, 1043, 1044, 1044, 1044, 1044, 1044, 1044, 1044, 1045, 1045, 1045, 1045, 1045, 1045, 1045, 1045, 1046, 1046, 1046, 1046, 1046, 1046, 1046, 1046, 1047, 1047, 1047, 1047, 1047, 1047, 1047, 1047, 1048, 1048, 1048, 1048, 1048, 1048, 1048, 1048, 1049, 1049, 1049, 1049, 1049, 1049, 1049, 1050, 1050, 1050, 1050, 1050, 1050, 1050, 1050, 1051, 1051, 1051, 1051, 1051, 1051, 1051, 1051, 1052, 1052, 1052, 1052, 1052, 1052, 1052, 1052, 1053, 1053, 1053, 1053, 1053, 1053, 1053, 1053, 1054, 1054, 1054, 1054, 1054, 1054, 1054, 1055, 1055, 1055, 1055, 1055, 1055, 1055, 1055, 1056, 1056, 1056, 1056, 1056, 1056, 1056, 1056, 1057, 1057, 1057, 1057, 1057, 1057, 1057, 1057, 1058, 1058, 1058, 1058, 1058, 1058, 1058, 1059, 1059, 1059, 1059, 1059, 1059, 1059, 1059, 1060, 1060, 1060, 1060, 1060, 1060, 1060, 1060, 1061, 1061, 1061, 1061, 1061, 1061, 1061, 1061, 1062, 1062, 1062, 1062, 1062, 1062, 1062, 1063, 1063, 1063, 1063, 1063, 1063, 1063, 1063, 1064, 1064, 1064, 1064, 1064, 1064, 1064, 1064, 1065, 1065, 1065, 1065, 1065, 1065, 1065, 1066, 1066, 1066, 1066, 1066, 1066, 1066, 1066, 1067, 1067, 1067, 1067, 1067, 1067, 1067, 1067, 1068, 1068, 1068, 1068, 1068, 1068, 1068, 1069, 1069, 1069, 1069, 1069, 1069, 1069, 1069, 1070, 1070, 1070, 1070, 1070, 1070, 1070, 1070, 1071, 1071, 1071, 1071, 1071, 1071, 1071, 1072, 1072, 1072, 1072, 1072, 1072, 1072, 1072, 1073, 1073, 1073, 1073, 1073, 1073, 1073, 1073, 1074, 1074, 1074, 1074, 1074, 1074, 1074, 1075, 1075, 1075, 1075, 1075, 1075, 1075, 1075, 1076, 1076, 1076, 1076, 1076, 1076, 1076, 1076, 1077, 1077, 1077, 1077, 1077, 1077, 1077, 1078, 1078, 1078, 1078, 1078, 1078, 1078, 1078, 1079, 1079, 1079, 1079, 1079, 1079, 1079, 1080, 1080, 1080, 1080, 1080, 1080, 1080, 1080, 1081, 1081, 1081, 1081, 1081, 1081, 1081, 928], 326983390450192912849303560, 326985365368118071617684139⟩
def ThetaRun0.s7 : Seg := ⟨326983390450192912849303560, 326985365368118071617684139, 17729241, 1048576, [1082, 1082, 1082, 1082, 1082, 1082, 1082, 1083, 1083, 1083, 1083, 1083, 1083, 1083, 1083, 1084, 1084, 1084, 1084, 1084, 1084, 1084, 1085, 1085, 1085, 1085, 1085, 1085, 1085, 1085, 1086, 1086, 1086, 1086, 1086, 1086, 1086, 1087, 1087, 1087, 1087, 1087, 1087, 1087, 1087, 1088, 1088, 1088, 1088, 1088, 1088, 1088, 1088, 1089, 1089, 1089, 1089, 1089, 1089, 1089, 1090, 1090, 1090, 1090, 1090, 1090, 1090, 1090, 1091, 1091, 1091, 1091, 1091, 1091, 1091, 1092, 1092, 1092, 1092, 1092, 1092, 1092, 1092, 1093, 1093, 1093, 1093, 1093, 1093, 1093, 1094, 1094, 1094, 1094, 1094, 1094, 1094, 1094, 1095, 1095, 1095, 1095, 1095, 1095, 1095, 1096, 1096, 1096, 1096, 1096, 1096, 1096, 1096, 1097, 1097, 1097, 1097, 1097, 1097, 1097, 1098, 1098, 1098, 1098, 1098, 1098, 1098, 1099, 1099, 1099, 1099, 1099, 1099, 1099, 1099, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1101, 1101, 1101, 1101, 1101, 1101, 1101, 1101, 1102, 1102, 1102, 1102, 1102, 1102, 1102, 1103, 1103, 1103, 1103, 1103, 1103, 1103, 1103, 1104, 1104, 1104, 1104, 1104, 1104, 1104, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1106, 1106, 1106, 1106, 1106, 1106, 1106, 1107, 1107, 1107, 1107, 1107, 1107, 1107, 1108, 1108, 1108, 1108, 1108, 1108, 1108, 1108, 1109, 1109, 1109, 1109, 1109, 1109, 1109, 1110, 1110, 1110, 1110, 1110, 1110, 1110, 1111, 1111, 1111, 1111, 1111, 1111, 1111, 1111, 1112, 1112, 1112, 1112, 1112, 1112, 1112, 1113, 1113, 1113, 1113, 1113, 1113, 1113, 1113, 1114, 1114, 1114, 1114, 1114, 1114, 1114, 1115, 1115, 1115, 1115, 1115, 1115, 1115, 1116, 1116, 1116, 1116, 1116, 1116, 1116, 1116, 1117, 1117, 1117, 1117, 1117, 1117, 1117, 1118, 1118, 1118, 1118, 1118, 1118, 1118, 1119, 1119, 1119, 1119, 1119, 1119, 1119, 1119, 1120, 1120, 1120, 1120, 1120, 1120, 1120, 1121, 1121, 1121, 1121, 1121, 1121, 1121, 1122, 1122, 1122, 1122, 1122, 1122, 1122, 1122, 1123, 1123, 1123, 1123, 1123, 1123, 1123, 1124, 1124, 1124, 1124, 1124, 1124, 1124, 1125, 1125, 1125, 1125, 1125, 1125, 1125, 1126, 1126, 1126, 1126, 1126, 1126, 1126, 1126, 1127, 1127, 1127, 1127, 1127, 1127, 1127, 1128, 1128, 1128, 1128, 1128, 1128, 1128, 1129, 1129, 1129, 1129, 1129, 1129, 1129, 1130, 1130, 1130, 1130, 1130, 1130, 1130, 1130, 1131, 1131, 1131, 1131, 1131, 1131, 1131, 1132, 1132, 1132, 1132, 1132, 1132, 1132, 1133, 1133, 1133, 1133, 1133, 1133, 1133, 1134, 1134, 1134, 1134, 1134, 1134, 1134, 1134, 1135, 1135, 1135, 1135, 1135, 1135, 1135, 1136, 1136, 1136, 1136, 1136, 1136, 1136, 1137, 1137, 1137, 1137, 1137, 1137, 1137, 1138, 1138, 1138, 1138, 1138, 1138, 1138, 1139, 1139, 1139, 1139, 1139, 1139, 1139, 1139, 1140, 1140, 1140, 1140, 1140, 1140, 1140, 1141, 1141, 1141, 1141, 1141, 1141, 1141, 1142, 1142, 1142, 1142, 1142, 1142, 1142, 1143, 1143, 1143, 1143, 1143, 1143, 1143, 1144, 1144, 1144, 1144, 1144, 1144, 1144, 1144, 1145, 1145, 1145, 1145, 1145, 1145, 1145, 1146, 1146, 1146, 1146, 1146, 1146, 1146, 1147, 1147, 1147, 1147, 1147, 1147, 1147, 1148, 1148, 1148, 1148, 1148, 1148, 1148, 1149, 1149, 1149, 1149, 1149, 1149, 1149, 1150, 1150, 1150, 1150, 1150, 1150, 1150, 1151, 1151, 1151, 1151, 1151, 1151, 1151, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1153, 1153, 1153, 1153, 1153, 1153, 1153, 1154, 1154, 1154, 1154, 1154, 1154, 1154, 1155, 1155, 1155, 1155, 1155, 1155, 1155, 1156, 1156, 1156, 1156, 1156, 1156, 1156, 1157, 1157, 1157, 1157, 1157, 1157, 1157, 1158, 1158, 1158, 1158, 1158, 1158, 1158, 1159, 1159, 1159, 1159, 1159, 1159, 1159, 1160, 1160, 1160, 1160, 1160, 1160, 1160, 1161, 1161, 1161, 1161, 1161, 1161, 1161, 1162, 1162, 1162, 1162, 1162, 1162, 1162, 1163, 1163, 1163, 1163, 1163, 1163, 1163, 1164, 1164, 1164, 1164, 1164, 1164, 1164, 1165, 1165, 1165, 1165, 1165, 1165, 1165, 1166, 1166, 1166, 1166, 1166, 1166, 1166, 1166, 1167, 1167, 1167, 1167, 1167, 1167, 1167, 1168, 1168, 1168, 1168, 1168, 1168, 1168, 1169, 1169, 1169, 1169, 1169, 1169, 1169, 1170, 1170, 1170, 1170, 1170, 1170, 1170, 1171, 1171, 1171, 1171, 1171, 1171, 1171, 1172, 1172, 1172, 1172, 1172, 1172, 1172, 1173, 1173, 1173, 1173, 1173, 1173, 1173, 1174, 1174, 1174, 1174, 1174, 1174, 1174, 1175, 1175, 1175, 1175, 1175, 1175, 1176, 1176, 1176, 1176, 1176, 1176, 1176, 1177, 1177, 1177, 1177, 1177, 1177, 1177, 1178, 1178, 1178, 1178, 1178, 1178, 1178, 1179, 1179, 1179, 1179, 1179, 1179, 1179, 1180, 1180, 1180, 1180, 1180, 1180, 1180, 1181, 1181, 1181, 1181, 1181, 1181, 1181, 1182, 1182, 1182, 1182, 1182, 1182, 1182, 1183, 1183, 1183, 1183, 1183, 1183, 1183, 1184, 1184, 1184, 1184, 1184, 1184, 1184, 1185, 1185, 1185, 1185, 1185, 1185, 1185, 1186, 1186, 1186, 1186, 1186, 1186, 1186, 1187, 1187, 1187, 1187, 1187, 1187, 1187, 1188, 1188, 1188, 1188, 1188, 1188, 1188, 1189, 1189, 1189, 1189, 1189, 1189, 1190, 1190, 1190, 1190, 1190, 1190, 1190, 1191, 1191, 1191, 1191, 1191, 1191, 1191, 1192, 1192, 1192, 1192, 1192, 1192, 1192, 1193, 1193, 1193, 1193, 1193, 1193, 1193, 1194, 1194, 1194, 1194, 1194, 1194, 1194, 1195, 1195, 1195, 1195, 1195, 1195, 1195, 1196, 1196, 1196, 1196, 1196, 1196, 1196, 1197, 1197, 1197, 1197, 1197, 1197, 1198, 1198, 1198, 1198, 1198, 1198, 1198, 1199, 1199, 1199, 1199, 1199, 1199, 1199, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1201, 1201, 1201, 1201, 1201, 1201, 1201, 1202, 1202, 1202, 1202, 1202, 1202, 1202, 1203, 1203, 1203, 1203, 1203, 1203, 1204, 1204, 1204, 1204, 1204, 1204, 1204, 1205, 1205, 1205, 1205, 1205, 1205, 1205, 1206, 1206, 1206, 1206, 1206, 1206, 1206, 1207, 1207, 1207, 1207, 1207, 1207, 1207, 1208, 1208, 1208, 1208, 1208, 1208, 1209, 1209, 1209, 1209, 1209, 1209, 1209, 377], 365649436534976799993366481, 365651693081491094014573814⟩

def ThetaRun0.segs : List Seg := [ThetaRun0.s0, ThetaRun0.s1, ThetaRun0.s2, ThetaRun0.s3, ThetaRun0.s4, ThetaRun0.s5, ThetaRun0.s6, ThetaRun0.s7]

end ThetaSieve
Source
P. Dusart, Estimates of some functions over primes without R.H., arXiv:1002.0442 (2010), Theorem 5.2 (k = 2, η = 0.2, x ≥ 3 594 641); here the range [3 594 641, 3 584 912 847] is closed by a kernel-checked sieve certificate.
View graph