Ramanujan's prime counting inequality holds for all x ≥ 38,358,837,683: ranges from the zeros, a spectral barrier, and trade-offs
Source files
root fileramanujan_inequality.tex · root file128 KiB · SHA-256 170f877ad8bacf54… · view textancillaryanc/README.txt1 KiB · SHA-256 02cbd9caf80af19b… · view textancillaryanc/barrier.py5 KiB · SHA-256 ec2374ca856c4710… · view textancillaryanc/buthe_bound.py5 KiB · SHA-256 acac6f587ac6c8f7… · view textancillaryanc/buthe_ramanujan.py7 KiB · SHA-256 a08e1344a3f312ff… · view textancillaryanc/buthe_reopt.py2 KiB · SHA-256 87bd845bdcf7b2dc… · view textancillaryanc/buthe_reopt_fine.py2 KiB · SHA-256 fa6b40b652caa17a… · view textancillaryanc/buthe_thesis_run.py308 B · SHA-256 eb3d85e6388b570d… · view textancillaryanc/ch_ramanujan.py6 KiB · SHA-256 9e035aa04dae94d5… · view textancillaryanc/confirm_theorem_D_thesis.py828 B · SHA-256 1f87597c595d20fb… · view textancillaryanc/crosscheck.py1 KiB · SHA-256 7e211f687b059fb6… · view textancillaryanc/crosscheck_buthe.py2 KiB · SHA-256 41bd913dbe5a01ec… · view textancillaryanc/downstream/bklnw_t15.py3 KiB · SHA-256 1a970b26c78b2b96… · view textancillaryanc/downstream/bklnw_t15_output.txt3 KiB · SHA-256 69bf6d3619d08878… · view textancillaryanc/downstream/cite_ctx.py1 KiB · SHA-256 8f5f7f5bdad832aa… · view textancillaryanc/downstream/e2_variants.py3 KiB · SHA-256 d29e55cc026afd34… · view textancillaryanc/downstream/extract_mupdf.py649 B · SHA-256 9a1930e6ea9d31d2… · view textancillaryanc/downstream/fks2_table6.py957 B · SHA-256 8cda850df9330cd1… · view textancillaryanc/downstream/fks2_table6_output.txt851 B · SHA-256 8626cda31fa1cf61… · view textancillaryanc/downstream/fks2_table7.py4 KiB · SHA-256 dbcdf1317a3b482a… · view textancillaryanc/downstream/fks2_table7_v2.py2 KiB · SHA-256 d54e088f85b7293c… · view textancillaryanc/downstream/fks2_table7_v2_output.txt3 KiB · SHA-256 657ea8c6a453a34c… · view textancillaryanc/downstream/grep_ctx.py994 B · SHA-256 36b006a0b3d18455… · view textancillaryanc/downstream/grep_ctx2.py1019 B · SHA-256 1a930a44c6970222… · view textancillaryanc/downstream/jlt_iter.py2 KiB · SHA-256 73be608ad3f0bfbb… · view textancillaryanc/downstream/jlt_iter_output.txt891 B · SHA-256 93c2a5994f32f4a1… · view textancillaryanc/downstream/jy_lemma23.py2 KiB · SHA-256 e39796664f1ae6ff… · view textancillaryanc/downstream/jy_lemma23_output.txt1 KiB · SHA-256 1778932bbd40de61… · view textancillaryanc/downstream/lp_e55_scan.py1 KiB · SHA-256 92786898d7632b43… · view textancillaryanc/downstream/lp_prop21.py2 KiB · SHA-256 42862ff84fd66116… · view textancillaryanc/downstream/lp_prop21_output.txt2 KiB · SHA-256 687dd9c63328026c… · view textancillaryanc/downstream/small_rows.py3 KiB · SHA-256 130c6d2eb0a6ec4d… · view textancillaryanc/downstream/summary_calcs.py3 KiB · SHA-256 fa2abf530e4859f8… · view textancillaryanc/downstream/summary_calcs_output.txt3 KiB · SHA-256 f4b025e1d6cc74cb… · view textancillaryanc/downstream/variants_table.py2 KiB · SHA-256 27dbf1bc5a21db4d… · view textancillaryanc/downstream/variants_table_output.txt2 KiB · SHA-256 c1a30c5acade1560… · view textancillaryanc/downstream/zeros_model.py3 KiB · SHA-256 1e848a9cfca11897… · view textancillaryanc/extend_ramanujan.py8 KiB · SHA-256 dbc3be413c80fd7c… · view textancillaryanc/fks_eps.py10 KiB · SHA-256 bbe755a851a6d33e… · view textancillaryanc/fks_eps_mpcheck.py2 KiB · SHA-256 5d1e5edfbe745f0b… · view textancillaryanc/fks_fine_R.py3 KiB · SHA-256 7f7a7f6dd5f8e606… · view textancillaryanc/hybrid_D.py2 KiB · SHA-256 5e6f138c4680d2fb… · view textancillaryanc/outputs/barrier_output.txt808 B · SHA-256 e18a4c9ab320a5d5… · view textancillaryanc/outputs/buthe_reopt_fine_output.txt559 B · SHA-256 03a18861131a926e… · view textancillaryanc/outputs/buthe_reopt_output.txt2 KiB · SHA-256 19c0289045922ec4… · view textancillaryanc/outputs/buthe_thesis_output.txt5 KiB · SHA-256 c3ffc4652c6513dc… · view textancillaryanc/outputs/ch_output.txt2 KiB · SHA-256 b1a36752a60e1524… · view textancillaryanc/outputs/confirm_D_thesis_output.txt327 B · SHA-256 98139dda8b7cf37b… · view textancillaryanc/outputs/crosscheck_buthe_output.txt2 KiB · SHA-256 e21829c8ed3adc20… · view textancillaryanc/outputs/crosscheck_output.txt892 B · SHA-256 324152dc0611d5a4… · view textancillaryanc/outputs/extend_output.txt1 KiB · SHA-256 ac29274429ed77e1… · view textancillaryanc/outputs/final_Bprime.txt699 B · SHA-256 44c0969b4ce2e0ef… · view textancillaryanc/outputs/final_C_BTYBEL.txt3 KiB · SHA-256 97d285cc68666079… · view textancillaryanc/outputs/final_C_BTYKLN.txt3 KiB · SHA-256 df7d564745d6e7f5… · view textancillaryanc/outputs/final_C_FKSR.txt2 KiB · SHA-256 6aeed4254825167f… · view textancillaryanc/outputs/final_C_MTY77.txt2 KiB · SHA-256 12da9604b42f1f56… · view textancillaryanc/outputs/final_C_PUB.txt2 KiB · SHA-256 7886923418a989b1… · view textancillaryanc/outputs/final_C_PUBBEL.txt2 KiB · SHA-256 fc749d8f1bccbccd… · view textancillaryanc/outputs/final_D_BTYBEL.txt804 B · SHA-256 0479aa3336059e39… · view textancillaryanc/outputs/final_D_PUB.txt903 B · SHA-256 b7e1d6a4aba5bc6c… · view textancillaryanc/outputs/qrh_ramanujan_output.txt373 B · SHA-256 66f297843ac5bd36… · view textancillaryanc/outputs/qrh_theta_output.txt786 B · SHA-256 27687f4b17de83fc… · view textancillaryanc/outputs/robust_Aref_K10.txt106 B · SHA-256 d9fd373e70782c7d… · view textancillaryanc/outputs/robust_Aref_K100.txt107 B · SHA-256 3c3c631bcded1d85… · view textancillaryanc/outputs/robust_Aref_K2.txt108 B · SHA-256 fe180c7beb330525… · view textancillaryanc/outputs/robust_Aref_K30.txt106 B · SHA-256 4513f229319b1e50… · view textancillaryanc/outputs/sens_K1.txt183 B · SHA-256 6191837059cc4103… · view textancillaryanc/outputs/sens_K10.txt186 B · SHA-256 ce9d55d512cec5b4… · view textancillaryanc/outputs/sens_K100.txt187 B · SHA-256 fa5ae83eff91aec4… · view textancillaryanc/outputs/sens_K1000.txt189 B · SHA-256 df067e8aabbc89d5… · view textancillaryanc/outputs/sens_K10000.txt191 B · SHA-256 3942dbd655311b83… · view textancillaryanc/outputs/sens_K1000000.txt195 B · SHA-256 cb6398b9f861df9a… · view textancillaryanc/outputs/tradeoff_R1.7373.txt149 B · SHA-256 878d272c018ee720… · view textancillaryanc/outputs/tradeoff_R2.0.txt956 B · SHA-256 fd5972e5df9efce4… · view textancillaryanc/outputs/tradeoff_R2.5.txt1 KiB · SHA-256 44b735c08939fcc2… · view textancillaryanc/outputs/tradeoff_R3.0.txt1 KiB · SHA-256 a7a258776150e081… · view textancillaryanc/outputs/tradeoff_R3.5.txt1 KiB · SHA-256 f63fa37db97c73f6… · view textancillaryanc/outputs/tradeoff_R4.0.txt1023 B · SHA-256 e843cf006bfda900… · view textancillaryanc/outputs/tradeoff_R4.896.txt1 KiB · SHA-256 2aa91481801515ca… · view textancillaryanc/outputs/tradeoff_R5.558691.txt1 KiB · SHA-256 4213741bd6e308b4… · view textancillaryanc/outputs/verify_output.txt3 KiB · SHA-256 ae7cdd01fae635ed… · view textancillaryanc/qrh_ramanujan.py3 KiB · SHA-256 6d1fe5ecd7b758df… · view textancillaryanc/qrh_theta.py2 KiB · SHA-256 84c8cba7eeacde03… · view textancillaryanc/robust_Aref.py580 B · SHA-256 6c017630b29c1828… · view textancillaryanc/sens_density.py2 KiB · SHA-256 048e561573532c95… · view textancillaryanc/tradeoff.py3 KiB · SHA-256 30f5c8d7f6641c3e… · view textancillaryanc/verify_ramanujan.py9 KiB · SHA-256 e73ce3ec081f8c72… · view textancillaryanc/zfr_B.py3 KiB · SHA-256 b1bf459fc48b55c3… · view text