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[4] File: illustrations/sarnak.jpg Graphic file (type jpg) Package pdftex.def Info: illustrations/sarnak.jpg used on input line 261. (pdftex.def) Requested size: 137.9979pt x 120.14143pt. Underfull \vbox (badness 10000) has occurred while \output is active [] [5 ] LaTeX Font Info: Try loading font information for OMS+cmr on input line 309. (/usr/share/texlive/texmf-dist/tex/latex/base/omscmr.fd File: omscmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <10> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 309. Overfull \hbox (7.23184pt too wide) in paragraph at lines 326--327 [][] [] Underfull \vbox (badness 10000) has occurred while \output is active [] [6 <./illustrations/sarnak.jpg>] File: illustrations/raoulbott.png Graphic file (type png) Package pdftex.def Info: illustrations/raoulbott.png used on input line 332. (pdftex.def) Requested size: 120.7521pt x 161.0015pt. 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[15 <./illustrations/factor_tree_6.pdf>] File: illustrations/factor_tree_300_a.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/factor_tree_300_a.pdf used on input line 570. (pdftex.def) Requested size: 162.15042pt x 79.41916pt. File: illustrations/factor_tree_300_b.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/factor_tree_300_b.pdf used on input line 570. (pdftex.def) Requested size: 162.15042pt x 79.41916pt. File: illustrations/factor_tree_big.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/factor_tree_big.pdf used on input line 5 72. (pdftex.def) Requested size: 345.0pt x 168.97588pt. 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[30] [31 <./illustrations/liouville-17.pdf> <./illustrations/liouville-100.pdf pdfTeX warning: pdflatex (file ./illustrations/liouville-100.pdf): PDF inclusio n: multiple pdfs with page group included in a single page > <./illustrations/liouville-1000.pdf pdfTeX warning: pdflatex (file ./illustrations/liouville-1000.pdf): PDF inclusi on: multiple pdfs with page group included in a single page > <./illustrations/liouville-10000.pdf pdfTeX warning: pdflatex (file ./illustrations/liouville-10000.pdf): PDF inclus ion: multiple pdfs with page group included in a single page > <./illustrations/liouville-100000.pdf pdfTeX warning: pdflatex (file ./illustrations/liouville-100000.pdf): PDF inclu sion: multiple pdfs with page group included in a single page > <./illustrations/liouville-1000000.pdf pdfTeX warning: pdflatex (file ./illustrations/liouville-1000000.pdf): PDF incl usion: multiple pdfs with page group included in a single page >] Chapter 7. File: illustrations/sieve200.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/sieve200.pdf used on input line 1377. (pdftex.def) Requested size: 276.00105pt x 135.18408pt. File: illustrations/proportion_primes_100.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/proportion_primes_100.pdf used on input line 1389. (pdftex.def) Requested size: 345.0pt x 168.96896pt. Underfull \vbox (badness 10000) has occurred while \output is active [] [32 <./illustrations/sieve200.pdf>] File: illustrations/proportion_primes_1000.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/proportion_primes_1000.pdf used on input line 1395. (pdftex.def) Requested size: 345.0pt x 169.74687pt. File: illustrations/proportion_primes_10000.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/proportion_primes_10000.pdf used on inpu t line 1396. (pdftex.def) Requested size: 345.0pt x 169.73842pt. 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(pdftex.def) Requested size: 276.00105pt x 82.83562pt. [36 <./illustrations/sieves7_100.pdf> <./illustrations/prime_pi_25_aspect1.pdf pdfTeX warning: pdflatex (file ./illustrations/prime_pi_25_aspect1.pdf): PDF in clusion: multiple pdfs with page group included in a single page > <./illustrations/prime_pi_100_aspect1.pdf pdfTeX warning: pdflatex (file ./illustrations/prime_pi_100_aspect1.pdf): PDF i nclusion: multiple pdfs with page group included in a single page >] Chapter 8. File: illustrations/prime_pi_1000.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/prime_pi_1000.pdf used on input line 147 6. (pdftex.def) Requested size: 276.00105pt x 135.6722pt. File: illustrations/prime_pi_10000.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/prime_pi_10000.pdf used on input line 14 77. (pdftex.def) Requested size: 276.00105pt x 135.56647pt. Underfull \vbox (badness 10000) has occurred while \output is active [] [37 <./illustrations/prime_pi_1000.pdf>] File: illustrations/prime_pi_100000.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/prime_pi_100000.pdf used on input line 1 479. (pdftex.def) Requested size: 276.00105pt x 135.558pt. [38 <./illustrations/prime_pi_10000.pdf> <./illustrations/prime_pi_100000.pdf pdfTeX warning: pdflatex (file ./illustrations/prime_pi_100000.pdf): PDF inclus ion: multiple pdfs with page group included in a single page >] Chapter 9. [39 ] [40] Chapter 10. File: illustrations/gauss.png Graphic file (type png) Package pdftex.def Info: illustrations/gauss.png used on input line 1548. (pdftex.def) Requested size: 103.50105pt x 132.6939pt. File: illustrations/pi_Li.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/pi_Li.pdf used on input line 1555. (pdftex.def) Requested size: 276.00105pt x 135.78476pt. [41 <./illustrations/gauss.png (PNG copy)> <./illustrations/pi_Li.pdf>] File: illustrations/log.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/log.pdf used on input line 1573. (pdftex.def) Requested size: 276.00105pt x 100.24481pt. File: illustrations/slide_rule.png Graphic file (type png) Package pdftex.def Info: illustrations/slide_rule.png used on input line 1593. (pdftex.def) Requested size: 276.00105pt x 53.6655pt. [42 <./illustrations/log.pdf>] File: illustrations/gauss_tables_half.png Graphic file (type png) Package pdftex.def Info: illustrations/gauss_tables_half.png used on input line 1606. (pdftex.def) Requested size: 310.4979pt x 246.00458pt. Underfull \vbox (badness 2189) has occurred while \output is active [] [43 <./illustrations/slide_rule.png> <./illustrations/gauss_tables_half.png>] File: illustrations/area_under_log_graph_30.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/area_under_log_graph_30.pdf used on inpu t line 1645. 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[47 ] File: illustrations/random_walks-3.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/random_walks-3.pdf used on input line 17 76. (pdftex.def) Requested size: 155.24895pt x 76.13002pt. File: illustrations/random_walks-3-mean.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/random_walks-3-mean.pdf used on input li ne 1776. (pdftex.def) Requested size: 155.24895pt x 76.34708pt. File: illustrations/random_walks-10.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/random_walks-10.pdf used on input line 1 778. (pdftex.def) Requested size: 155.24895pt x 76.39569pt. File: illustrations/random_walks-10-mean.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/random_walks-10-mean.pdf used on input l ine 1778. (pdftex.def) Requested size: 155.24895pt x 76.34708pt. File: illustrations/random_walks-100.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/random_walks-100.pdf used on input line 1780. 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File: illustrations/three_plots.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/three_plots.pdf used on input line 1814. (pdftex.def) Requested size: 310.4979pt x 112.6158pt. Underfull \vbox (badness 10000) has occurred while \output is active [] [49 ] [50 <./illustrations/three_plots.pdf>] Chapter 14. [51 ] Chapter 15. File: illustrations/camaro.png Graphic file (type png) Package pdftex.def Info: illustrations/camaro.png used on input line 1897. (pdftex.def) Requested size: 241.49895pt x 91.8178pt. [52 <./illustrations/camaro.png>] File: illustrations/cesaro.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/cesaro.pdf used on input line 1906. (pdftex.def) Requested size: 310.4979pt x 152.44196pt. [53 <./illustrations/cesaro.pdf>] Chapter 16. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 1907. 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(pdftex.def) Requested size: 120.7521pt x 163.41455pt. [55 <./illustrations/littlewood.png>] Chapter 17. Overfull \hbox (1.5503pt too wide) in paragraph at lines 1935--1940 \OT1/cmr/m/n/10 Take a look at Fig-ure []13.1[] again. All three func-tions, $[ ](\OML/cmm/m/it/10 X\OT1/cmr/m/n/10 )$, $\OML/cmm/m/it/10 ^^Y\OT1/cmr/m/n/10 (\ OML/cmm/m/it/10 X\OT1/cmr/m/n/10 )$ and $\OML/cmm/m/it/10 X= []\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X\OT1/cmr/m/n/10 )$ [] File: illustrations/similar_rates.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/similar_rates.pdf used on input line 197 0. (pdftex.def) Requested size: 345.0pt x 125.14497pt. [56 ] File: illustrations/same_rates.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/same_rates.pdf used on input line 1982. (pdftex.def) Requested size: 345.0pt x 125.54152pt. [57 <./illustrations/similar_rates.pdf> <./illustrations/same_rates.pdf>] File: illustrations/riemann_zoom.png Graphic file (type png) Package pdftex.def Info: illustrations/riemann_zoom.png used on input line 2048 . (pdftex.def) Requested size: 345.0pt x 65.94928pt. File: illustrations/riemann.png Graphic file (type png) Package pdftex.def Info: illustrations/riemann.png used on input line 2058. (pdftex.def) Requested size: 103.50105pt x 110.1065pt. Underfull \vbox (badness 7777) has occurred while \output is active [] [58 <./illustrations/riemann_zoom.png (PNG copy)>] [59 <./illustrations/rieman n.png (PNG copy)>] Chapter 18. File: illustrations/PN_25.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/PN_25.pdf used on input line 2089. (pdftex.def) Requested size: 137.9979pt x 67.96352pt. File: illustrations/PN_100.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/PN_100.pdf used on input line 2090. 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Underfull \vbox (badness 10000) has occurred while \output is active [] [60 ] [61 <./illustrations/PN_25.pdf> <./illustrations/PN_100.pdf pdfTeX warning: pdflatex (file ./illustrations/PN_100.pdf): PDF inclusion: mult iple pdfs with page group included in a single page > <./illustrations/PN_1000.pdf pdfTeX warning: pdflatex (file ./illustrations/PN_1000.pdf): PDF inclusion: mul tiple pdfs with page group included in a single page > <./illustrations/PN_10000.pdf pdfTeX warning: pdflatex (file ./illustrations/PN_10000.pdf): PDF inclusion: mu ltiple pdfs with page group included in a single page > <./illustrations/PN_100000.pdf pdfTeX warning: pdflatex (file ./illustrations/PN_100000.pdf): PDF inclusion: m ultiple pdfs with page group included in a single page >] Chapter 19. [62 ] File: illustrations/psi_9.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/psi_9.pdf used on input line 2167. (pdftex.def) Requested size: 135.6085pt x 148.50235pt. File: illustrations/psi_100.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/psi_100.pdf used on input line 2167. (pdftex.def) Requested size: 163.12039pt x 148.50235pt. File: illustrations/psi_diag_1000.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/psi_diag_1000.pdf used on input line 219 6. (pdftex.def) Requested size: 258.75pt x 232.30362pt. [63 <./illustrations/psi_9.pdf> <./illustrations/psi_100.pdf pdfTeX warning: pdflatex (file ./illustrations/psi_100.pdf): PDF inclusion: mul tiple pdfs with page group included in a single page >] [64 <./illustrations/psi_diag_1000.pdf>] Chapter 20. File: illustrations/sin.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/sin.pdf used on input line 2230. (pdftex.def) Requested size: 241.49895pt x 117.92107pt. 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File: illustrations/rainbow.png Graphic file (type png) Package pdftex.def Info: illustrations/rainbow.png used on input line 2385. (pdftex.def) Requested size: 68.99895pt x 126.46281pt. [71 <./illustrations/rainbow.png>] [72] Chapter 22. File: illustrations/pure_tone.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/pure_tone.pdf used on input line 2409. (pdftex.def) Requested size: 241.49895pt x 87.96327pt. File: illustrations/mixed_tone3.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/mixed_tone3.pdf used on input line 2422. (pdftex.def) Requested size: 241.49895pt x 87.9597pt. Underfull \vbox (badness 1163) has occurred while \output is active [] [73 <./illustrations/pure_tone.pdf>] [74 <./illustrations/mixed_tone3.pdf>] Chapter 23. File: illustrations/prime_pi_100_aspect1.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/prime_pi_100_aspect1.pdf used on input l ine 2442. (pdftex.def) Requested size: 327.74895pt x 98.36761pt. [75 ] [76] Chapter 24. [77 ] [78 ] Chapter 25. File: illustrations/newton.png Graphic file (type png) Package pdftex.def Info: illustrations/newton.png used on input line 2541. (pdftex.def) Requested size: 86.25pt x 109.53795pt. File: illustrations/leibniz.png Graphic file (type png) Package pdftex.def Info: illustrations/leibniz.png used on input line 2541. (pdftex.def) Requested size: 86.25pt x 108.99332pt. [79 <./illustrations/newton.png> <./illustrations/leibniz.png>] File: illustrations/graph_aplusone.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/graph_aplusone.pdf used on input line 25 65. (pdftex.def) Requested size: 207.0021pt x 101.38806pt. File: illustrations/graph_slope_deriv.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/graph_slope_deriv.pdf used on input line 2574. (pdftex.def) Requested size: 345.0pt x 168.97588pt. 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[84 <./illustrations/weierstrass.png (PNG copy)> <./illustrations/schwartz.png (PNG copy)>] [85] Chapter 26. File: illustrations/dirac.png Graphic file (type png) Package pdftex.def Info: illustrations/dirac.png used on input line 2783. (pdftex.def) Requested size: 103.50105pt x 146.37874pt. Underfull \vbox (badness 10000) has occurred while \output is active [] [86 ] File: illustrations/oo_integral.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/oo_integral.pdf used on input line 2815. (pdftex.def) Requested size: 276.00105pt x 88.53757pt. [87 <./illustrations/dirac.png (PNG copy)> <./illustrations/oo_integral.pdf>] [88] File: illustrations/dirac_delta.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/dirac_delta.pdf used on input line 2890. (pdftex.def) Requested size: 172.5pt x 84.48793pt. [89 <./illustrations/dirac_delta.pdf>] File: illustrations/simple_staircase.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/simple_staircase.pdf used on input line 2971. (pdftex.def) Requested size: 207.0021pt x 101.31355pt. [90] [91 <./illustrations/simple_staircase.pdf>] Chapter 27. File: illustrations/even_function.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/even_function.pdf used on input line 300 4. (pdftex.def) Requested size: 276.00105pt x 88.58258pt. File: illustrations/even_pi.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/even_pi.pdf used on input line 3015. (pdftex.def) Requested size: 276.00105pt x 79.65752pt. [92 <./illustrations/even_function.pdf>] File: illustrations/fourier_machine.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/fourier_machine.pdf used on input line 3 038. (pdftex.def) Requested size: 207.0021pt x 101.38806pt. [93 <./illustrations/even_pi.pdf> <./illustrations/fourier_machine.pdf pdfTeX warning: pdflatex (file ./illustrations/fourier_machine.pdf): PDF inclus ion: multiple pdfs with page group included in a single page >] [94] Chapter 28. [95 ] File: illustrations/two_delta.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/two_delta.pdf used on input line 3109. (pdftex.def) Requested size: 137.9979pt x 70.3002pt. [96 <./illustrations/two_delta.pdf>] Chapter 29. File: illustrations/two_delta.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/two_delta.pdf used on input line 3176. (pdftex.def) Requested size: 137.9979pt x 70.3002pt. [97 ] [98] Chapter 30. [99 ] File: illustrations/mini_phihat_even.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/mini_phihat_even.pdf used on input line 3266. (pdftex.def) Requested size: 345.0pt x 111.29192pt. 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Underfull \vbox (badness 4995) has occurred while \output is active [] [106 <./illustrations/primes_line.pdf>] [107 <./illustrations/PN_38.pdf>] [108] Chapter 32. File: illustrations/bigPhi.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/bigPhi.pdf used on input line 3552. (pdftex.def) Requested size: 345.0pt x 126.18637pt. [109 ] File: illustrations/theta_3_intro-1.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/theta_3_intro-1.pdf used on input line 3 584. (pdftex.def) Requested size: 293.2521pt x 143.98773pt. [110 <./illustrations/bigPhi.pdf>] File: illustrations/theta_3_intro-2.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/theta_3_intro-2.pdf used on input line 3 594. (pdftex.def) Requested size: 293.2521pt x 144.00467pt. File: illustrations/theta_C-3.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/theta_C-3.pdf used on input line 3600. (pdftex.def) Requested size: 310.4979pt x 152.99889pt. 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[113 <./illustrations/theta_C-20.pdf> <./illustrations/theta_C-100.pdf pdfTeX warning: pdflatex (file ./illustrations/theta_C-100.pdf): PDF inclusion: multiple pdfs with page group included in a single page > <./illustrations/theta_C-200.pdf pdfTeX warning: pdflatex (file ./illustrations/theta_C-200.pdf): PDF inclusion: multiple pdfs with page group included in a single page > <./illustrations/theta_C-500.pdf pdfTeX warning: pdflatex (file ./illustrations/theta_C-500.pdf): PDF inclusion: multiple pdfs with page group included in a single page >] Chapter 33. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 3744. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\theta' on input line 3744. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `subscript' on input line 3744. 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(pdftex.def) Requested size: 137.9979pt x 67.68475pt. File: illustrations/zero-spacing-mod1.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/zero-spacing-mod1.pdf used on input line 3832. (pdftex.def) Requested size: 137.9979pt x 67.71437pt. [117 <./illustrations/zero-spacing-mod2pi.pdf> <./illustrations/zero-spacing-mod1.p df pdfTeX warning: pdflatex (file ./illustrations/zero-spacing-mod1.pdf): PDF incl usion: multiple pdfs with page group included in a single page >] File: illustrations/riemann_spectrum_gaps.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/riemann_spectrum_gaps.pdf used on input line 3843. (pdftex.def) Requested size: 327.74895pt x 160.52792pt. Overfull \hbox (26.98589pt too wide) has occurred while \output is active \OT1/cmr/m/n/10 118 \OT1/cmr/m/sl/10 CHAPTER 34. FURTHER QUESTIONS ABOUT THE R IEMANN SPECTRUM [] [118 <./illustrations/riemann_spectrum_gaps.pdf>] Chapter 35. 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(pdftex.def) Requested size: 310.4979pt x 152.29684pt. File: illustrations/Rk_50_350_400.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/Rk_50_350_400.pdf used on input line 408 8. (pdftex.def) Requested size: 310.4979pt x 105.62292pt. [127 <./illustrations/Rk_50_2_100.pdf> <./illustrations/Rk_50_2_500.pdf pdfTeX warning: pdflatex (file ./illustrations/Rk_50_2_500.pdf): PDF inclusion: multiple pdfs with page group included in a single page > <./illustrations/Rk_50_350_400.pdf pdfTeX warning: pdflatex (file ./illustrations/Rk_50_350_400.pdf): PDF inclusio n: multiple pdfs with page group included in a single page >] Chapter 37. [128 ] Overfull \hbox (4.83286pt too wide) in paragraph at lines 4122--4126 []\OT1/cmr/m/n/10 The Wikipedia en-try for Rie-mann's Zeta Func-tion[] ([]$\OT1 /cmtt/m/n/10 http : / / en . wikipedia . 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File: illustrations/gaussian_staircase_10000.pdf Graphic file (type pdf) Package pdftex.def Info: illustrations/gaussian_staircase_10000.pdf used on inp ut line 4453. (pdftex.def) Requested size: 276.00105pt x 171.0593pt. Underfull \vbox (badness 10000) has occurred while \output is active [] [138 <./illustrations/gaussian_staircase_14.pdf> <./illustrations/gaussian_sta ircase_100.pdf>] [139 <./illustrations/gaussian_staircase_1000.pdf> <./illustra tions/gaussian_staircase_10000.pdf>] [140] (./rh.bbl [141 ] Underfull \hbox (badness 5667) in paragraph at lines 69--76 []\OT1/cmr/m/n/10 The page []$\OT1/cmtt/m/n/10 http : / / en . wikipedia . org / wiki / Integer _ factorization _ [] [142] LaTeX Font Info: Try loading font information for OMS+cmss on input line 85. LaTeX Font Info: No file OMScmss.fd. on input line 85. LaTeX Font Warning: Font shape `OMS/cmss/m/n' undefined (Font) using `OMS/cmsy/m/n' instead (Font) for symbol `textbullet' on input line 85. 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[] [143] Underfull \hbox (badness 10000) in paragraph at lines 113--114 [] Overfull \hbox (19.89217pt too wide) in paragraph at lines 143--147 []$\OML/cmm/m/it/10 n \OT1/cmr/m/n/10 = 123018668453011775513049495838496272077 28535695953347921973224521[] [] Overfull \hbox (20.55666pt too wide) in paragraph at lines 143--147 \OT1/cmr/m/n/10 517264005072636575187452021997864693899564749427740638459251925 573263[] [] Overfull \hbox (20.55666pt too wide) in paragraph at lines 143--147 \OT1/cmr/m/n/10 034537315482685079170261221429134616704292143116022212404792747 377940[] [] Overfull \hbox (26.1433pt too wide) in paragraph at lines 148--150 $\OML/cmm/m/it/10 p \OT1/cmr/m/n/10 = 3347807169895689878604416984821269081770 47949837137685689124313889[] [] Overfull \hbox (25.93495pt too wide) in paragraph at lines 151--153 $\OML/cmm/m/it/10 q \OT1/cmr/m/n/10 = 3674604366679959042824463379962795263227 91581643430876426760322838[] [] [144] Underfull \hbox (badness 1521) in paragraph at lines 182--193 []\OT1/cmr/m/n/10 In Sage, the func-tion \OT1/cmtt/m/n/10 prime[]range \OT1/cmr /m/n/10 enu-mer-ates primes in a range. 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