{"query": "The primes and the nucleus — one statistical fingerprint", "count": 20, "results": [{"id": "card_n_ea9e3f380756", "title": "The primes and the nucleus — one statistical fingerprint", "shelf": "science", "surface": "secular", "snippet": "The night's deepest rhyme, and it is real, published, and unexplained. Montgomery (1973)\nand Dyson noticed that the SPACINGS between the Riemann zeta zeros follow the same distribution\nas the eigenval"}, {"id": "card_c_741715d501d0", "title": "The primes and the nucleus — one statistical ↔ Primes and zeta — Euler's bridge and the pri", "shelf": "connections", "surface": null, "snippet": "A prime number and a uranium nucleus carry the same deep statistical signature.  — a concord the card itself states; mined + verified."}, {"id": "card_c_59abe461b1af", "title": "The primes and the nucleus — one statistical ↔ The nucleus — the strongest glue and the slo", "shelf": "connections", "surface": null, "snippet": "the very statistics that describe the ENERGY LEVELS of heavy nuclei and quantum chaos ... A prime number and a uranium nucleus carry the same deep statistical signature.  — a concord the card itself s"}, {"id": "card_src_oeis_a000928", "title": "A000928 — Irregular primes: primes p such that at least one of the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) is divisible by p.", "shelf": "oeis", "surface": "secular", "snippet": "Irregular primes: primes p such that at least one of the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) is divisible by p.  First terms: 37, 59, 67, 101, 103, 131, 149, 157, 233,"}, {"id": "card_n_639fcf317634", "title": "Primes and zeta — Euler's bridge and the prime number theorem", "shelf": "science", "surface": "secular", "snippet": "Euler tied the primes to the continuum: zeta(s) = product over primes of 1/(1-p^-s), so a\nstatement about ALL integers becomes a statement about the primes. Sealed: there are exactly 25\nprimes below 1"}, {"id": "card_n_1b6fc0a79c10", "title": "Ignatius to the Magnesians VII", "shelf": "patristics", "surface": "witness", "snippet": "As therefore the Lord did nothing without the Father, being united to Him, neither by Himself nor by the apostles, so neither do ye anything without the bishop and presbyters. Neither endeavour that a"}, {"id": "card_src_oeis_a001259", "title": "A001259 — A sequence of sorted odd primes 3 = p_1 < p_2 < ... < p_m such that p_i-2 divides the product p_1*p_2*...*p_(i-1) of the earlier primes and each prime factor of p_i-1 is ", "shelf": "oeis", "surface": "secular", "snippet": "A sequence of sorted odd primes 3 = p_1 < p_2 < ... < p_m such that p_i-2 divides the product p_1*p_2*...*p_(i-1) of the earlier primes and each prime factor of p_i-1 is a prime factor of twice the pr"}, {"id": "card_n_53c81d366707", "title": "The Chalcedonian Definition", "shelf": "codex", "surface": "witness", "snippet": "Following the holy fathers, we all with one accord teach men to acknowledge one and the same Son, our Lord Jesus Christ, at once complete in Godhead and complete in manhood, truly God and truly man, c"}, {"id": "card_n_137e090d24e8", "title": "Aurelius, Meditations §aur_04_xxxiii: Ever consider and think upon the world as being but one living substance, and...", "shelf": "classics", "surface": "secular", "snippet": "Ever consider and think upon the world as being but one living substance, and having but one soul, and how all things in the world, are terminated into one sensitive power; and are done by one general"}, {"id": "card_src_book_61473", "title": "Is a Ship Canal Practicable? Notes, Historical and Statistical, Upon the Projected Routes for an Interoceanic Ship Canal Between the Atlantic and Pacific Oceans, in Which is Includ", "shelf": "gutenberg", "surface": "secular", "snippet": "Is a Ship Canal Practicable? Notes, Historical and Statistical, Upon the Projected Routes for an Interoceanic Ship Canal Between the Atlantic and Pacific Oceans, in Which is Included a Short Account o"}, {"id": "card_c_90d08d3e378d", "title": "The primes and the nucleus — one statistical ↔ Numbers in the text and in the world — the h", "shelf": "connections", "surface": null, "snippet": "It is the clearest instance of the thread: numbers, in the physical.  — a concord the card itself states; mined + verified."}, {"id": "card_n_247becdb1217", "title": "Pirkei Avot §avot_06_01: The sages taught in the language of the Mishnah.", "shelf": "classics", "surface": "secular", "snippet": "The sages taught in the language of the Mishnah. Blessed be He who chose them and their teaching. Rabbi Meir said: Whoever occupies himself with the Torah for its own sake, merits many things; not onl"}, {"id": "card_src_oeis_a005115", "title": "A005115 — Let i, i+d, i+2d, ..., i+(n-1)d be an n-term arithmetic progression of primes; choose the one which minimizes the last term; then a(n) = last term i+(n-1)d.", "shelf": "oeis", "surface": "secular", "snippet": "Let i, i+d, i+2d, ..., i+(n-1)d be an n-term arithmetic progression of primes; choose the one which minimizes the last term; then a(n) = last term i+(n-1)d.  First terms: 2, 3, 7, 23, 29, 157, 907, 16"}, {"id": "card_n_05b8128f5115", "title": "Aurelius, Meditations §aur_07_vi: Let not things future trouble thee.", "shelf": "classics", "surface": "secular", "snippet": "Let not things future trouble thee. For if necessity so require that they come to pass, thou shalt (whensoever that is) be provided for them with the same reason, by which whatsoever is now present, i"}, {"id": "card_c_25f0eae28355", "title": "The primes and the nucleus — one statistical ↔ The Riemann hypothesis — sealed all around, ", "shelf": "connections", "surface": null, "snippet": "the SPACINGS between the Riemann zeta zeros follow the same distribution as the eigenvalue spacings of large random Hermitian matrices (the Gaussian Unitary Ensemble)  — a concord the card itself stat"}, {"id": "card_n_30f07d4a57c4", "title": "1 Clement XLVI", "shelf": "patristics", "surface": "witness", "snippet": "Such examples, therefore, brethren, it is right that we should follow; since it is written, “Cleave to the holy, for those that cleave to them shall [themselves] be made holy.” And again, in another p"}, {"id": "card_n_329e521d766b", "title": "Aurelius, Meditations §aur_06_xxxiii: Asia, Europe; what are they, but as corners of the whole world; of which the ...", "shelf": "classics", "surface": "secular", "snippet": "Asia, Europe; what are they, but as corners of the whole world; of which the whole sea, is but as one drop; and the great Mount Athos, but as a clod, as all present time is but as one point of eternit"}, {"id": "card_n_1a75580d235c", "title": "Genesis 1", "shelf": "codex", "surface": "witness", "snippet": "1. In the beginning, God created the heavens and the earth.\n2. The earth was formless and empty. Darkness was on the surface of the deep and God’s Spirit was hovering over the surface of the waters.\n3"}, {"id": "card_n_63ef068c22b2", "title": "Sermon on the Mount §som_13_treasures_in_heaven_one_master: \"Don't lay up treasures for yourselves on the earth, where moth and rust cons...", "shelf": "codex", "surface": "witness", "snippet": "\"Don't lay up treasures for yourselves on the earth, where moth and rust consume, and where thieves break through and steal; but lay up for yourselves treasures in heaven, where neither moth nor rust "}, {"id": "card_n_0eb13fc4e133", "title": "Imitation of Christ §imit_01_03: Happy is the man whom Truth by itself doth teach, not by figures and transien...", "shelf": "classics", "surface": "witness", "snippet": "Happy is the man whom Truth by itself doth teach, not by figures and transient words, but as it is in itself.(1) Our own judgment and feelings often deceive us, and we discern but little of the truth."}]}