International Journal of Applied Mathematical Research, 2 (4) (2013) 423-438 ©Science Publishing Corporation www.sciencepubco.com/index.php/IJAMR The primordial end calculus of prime numbers and mathematics Vinoo Cameron Hope research, Athens, Wisconsin, USA E-mail:[email protected] Abstract This Manuscript on the end primordial calculus of mathematics is a new discovery of the spiral nature of the entire mathematical grid at 1:3 by the precise and absolute concordance of regular number spirals and the Prime number spirals based on numbers and their spaces by grid. It is exclusive to IJAMR which has published 8 papers of the author on this new mathematics. The manuscript has NOT been offered to any other journal in the world .The editorial board of Princeton University, USA, Annals of mathematics had been duly informed by letter of the new discovery of the concordance of prime numbers spirals with regular number spirals, but for the sake of fidelity. Mathematics is not complexity, but simplicity, the configuration of 1 is spiral .The relationship between pure mathematical numbers and empty space is a primordial relationship, and well defined by gaps, plus it has been validated by the author by the Publishing of the pure continuous Den-Otter Prime number sieve at 1/6 and 5/6 ( and 1/3 and 2/3),and these prime sieves are reversible .Thus the relationship of the configuration of 1 is in two planes that expand in the frame of (5/6 and 1/6 ) and (1/3 and 2/3)are represented by spiral configuration , expressed by these numbers, as in :All prime numbers spirals are assigned infinitely by the simple -1 offset of the two spiral numbers cords 1/3+2/3=1 5/6+1/6=1 1/3-1/6=1/6 5/6-2/3=1/6 1/3+1/6=0.5 5/6+2/3=1.5 1.5/0.5=3 Note: the above is also confirmed by Arabian numerical shown below. Primordial mathematics as created by the creator is absolute and precise whilst the mathematics invented by man is approximate .Current Mathematics of a thousand years has accomplished much by approximate theory, and it is very possible to land a man on the moon by approximate mathematics, but to precisely understand mass and energy, the nucleus of mass and the vastness of space, one must understand the precise nature and curvature of space. Space and mathematics are curved precisely at 1:3 from primordial times( the basis for the π as shown under the publication Unified Theorem), and the warping of space is related to the 1:3 separation at precise 19 correct degrees separation and the precise right angled separation at 1:3 is at 360/19 degrees. This mathematics is about the curved lay of the grid of mathematics and cannot be understood by the current linear obsession of mathematics, but the readers are immediately referred to the 8 published papers of the author as referenced below. The calculus below virtually negates the current mathematics ideas of linear ascension theories of the past 500 years. This calculus is true for all prime numbers. This involves a precise “combing” of all prime number spirals around a half line. This is clearly and singularly the solution to prime number spiral calculus, which is fairly simple after this discovery. The ruminations of George Riemann and others of the past 500 years in linear ascension mathematics of prime numbers are non- functional irrelevant mathematics, just collateral observations of the correct mathematics which is presented here as “Primum movens” of mathematics. In Mathematics there is only a single best resolution, whilst collateral equations abound, as they have for 500 years for prime numbers which we have proved are basically by two chords and ascend by a half-line. Einstein’s observations and ruminations likewise are collateral and not central to the fact that the universe is precisely curved, and ascension of prime numbers are by two spiral chords. Keywords: Spirals of Prime numbers, Concordance of Prime numbers and natural numbers, Prime number spiral calculus. 424 International Journal of Applied Mathematical Research 1 Introduction This massive mathematics can only be introduced by the published references provided below. Basically the entire mathematics is at 1:3 at 19 correct degrees by spatial configuration which is shown under. The basic novel continuous Prime number sieve at 1:3, at (5/6: 1/6) and (2/3:1/3) has been recently published, yet unnoticed. It is the Den- Otter prime sieve and is reversible The word “Spiral” for the purposes of this paper indicates the three numbers of concordant gaps around a prime number. The symbol (n_) represents a gap between numbers as an example for the prime number 11 the following are the spiral gaps. By regular numbers at prime number 11: 9_11_13 By prime numbers at prime number 11: 5_11_17 The Basic Mathematics of concordance of spiral numbers is at gaps 12 and gap 4 as in the example above (9+11+13)=(5+11+17)=33 for regular numbers and is the base at (12/4=3) and the fact that at this grid alone the total additional values for the regular spiral numbers at 4 span equal those of the Prime number spirals at 12 span, as shown further below, and is a constant, so is the constant 32 .The mentioned Spiral constants are constant throughout the entire mathematical grid between the Prime number spirals and the regular prime number spirals as follows, at the half line( Spiral gap 10,12,14,16,18,20,22,24, 26, 28,30……………..and so on. 1.1 Spiral progression of numbers/prime numbers by gap value Constant 4 and 12 (example for prime numbers 19, 41, 43...) 13_19_29 17_19_21 (29*19)- (13*19) =304 (21*19)- (17*19) =76 304/76=4 304-76=228 228/19=12 31_41_47 39_41_43 (47*41)- (41*31) =656 (43*41)- (39*41) =164 656/164=4 656-164=492 492/41=12 37_43_53 41_43*45 (53*43)- (43*37) =688 (45*43)-43*41) =172 688/172=4 688-172=516 516/43=12 67_73_83 71_73_75 (83*73)- (73*71) =1168 (75*73)- (73*71=292 1168/292=4 1168-292=876 876/73=12 Gap 18 spirals: Constant 4.5 and 14(example prime numbers 29, 31, 47) 17_29_37 27_29_31 (37*29)- (29*19) =522 ((29*31)-(29*27) =116 522/16=4.5 522-116=406 406/29=14 23_31_41 29_31_33 (41*31)- (31*23) = 558 International Journal of Applied Mathematical Research 425 (33*31-(29*31) =124 558/124=4.5 558-124=434 434/31=14 41_47_59 45_47_49 (59*47)- (47*41) =846 (49*47)- (47*45) =188 846/188=4.5 846-188=658 658/47=14 Gap Spiral 20: Constant 5 and 16 (example Prime numbers 59, 97, 139, 151) 47_59_67 57_59_61 (67*59)- (59*47) =1180 (59*61)- (59*57) =236 1180/236=5 1180-236=944 944/59=16 83_97_103 95_97_99 (103*97)- (97*83) =1940 (99*97)- (95*97=388 1940/388=5 1940-388=1552 1552/97=16 131_139_151 95_97_99 (151*139)- (139*131) =2780 (141*139)- (139*137) =556 2780/556=5 2780-556=2224 2224/139=16 1.2 Indirect assignment of all spiral values of prime numbers by the offset of prime number dual chains at -1 Please note the -1base offset arrangement that delineate the spiral values for each prime number. Precise values are obtained from the new continuous Prime number sieve at 5/6, 1/6 and 1/3, 2/3(Den-Otter prime number Sieve recently published by the author).The spiral gap is indicated as Prime number (spiral span) Spiral gap 1 5 (10) 11 3 7 (10) 13 5 11 (12) 17 7 13 (12) 19 11 17 (12) 23 13 19 (16) 29 17 23 (14) 31 19 29 (18) 37 23 31 (18) 41 29 37 (14) 43 31 41 (16) 47 37 43 (16) 53 41 47 (18) 59 43 53 (18) 61 47 59 (20) 67 53 61 (18) 71 59 67 (14) 73 61 71 (18) 79 426 International Journal of Applied Mathematical Research 67 73 (16) 83 71 79 (18) 89 73 83 (24) 97 79 89 (22) 101 83 97 (20) 103 89 101 (18) 107 97 103 (12) 109 101 107 (12) 113 103 109 (24) 127 107 113 (24) 131 109 127 (28) 137 113 131 (26) 139 127 137 (22) 149 131 139 (20) 151 137 149 (20) 157 139 151 (24) 163 149 157 (18) 167 151 163 (22) 173 157 167 (22) 179 163 173 (18) 181 167 179 (24 191 173 181 (20) 193 179 191 (18) 197 181 193 (18) 199 191 197 (20) 211 193 199 (30) 223 197 211 (30) 227 199 223 (30) 229 211 227 (22) 233 223 229 (16) 239 227 233 (14) 241 229 239 (22) 251 233 241 (24) 257 239 251 (24) 263 241 257 (28) 269 251 263 (20) 271 257 269 (20) 277 263 271 (18) 281 269 277(14) 283 271 281(22) 293 277 283 (36) 307 281 293 (34) 311 283 307(30) 313 293 311 (24) 317 307 313 (24) 331 311 317 (26) 337 313 331 (34) 347 317 337 (32) 349 331 347 (22) 353 337 349 (22) 359 347 353 (20) 367 349 359 (24) 373 353 367 (26) 379 359 373 (24) 383 367 379 (22) 389 373 383 (24) 397 379 389 (22) 401 383 397 (26) 409 389 401 (30) 419 397 409 (24) 421 International Journal of Applied Mathematical Research 427 401 419 (30) 431 409 421 (24) 433 419 431 (20) 439 421 433 (22) 443 431 439 (18) 449 433 443 (24) 457 439 449 (22) 461 443 457 (20) 463 449 461 (18) 467 457 463 (22) 479 461 467 (26) 487 463 479 (28) 491 467 487 (32) 499 479 491 (24) 503 487 499 (22) 509 491 503 (30) 521 499 509 (24) 523 503 521 (38) 541 509 523 (38) 547 521 541 (36) 557 523 547 (40) 563 541 557 (29) 569 547 563 (24) 571 557 569 (20) 577 563 571 (24) 587 569 577 (24) 593 571 587 (28) 599 577 593 (24) 601 587 599 (20) 607 593 601 (20) 613 599 607 (18) 617 601 613 (18) 619 607 617 (24) 631 613 619 (28) 641 617 631 (26) 643 619 641 (28) 647 631 643 (22) 653 641 647 (18) 659 643 653 (18) 661 647 659 (26) 673 653 661 (24) 677 659 673 (24) 683 661 677 (30) 691 673 683 (28) 701 677 691 (32) 709 683 701 (36) 719 691 709 (36) 727 701 719 (32) 733 709 727 (30) 739 719 733 (24) 743 727 739 (24) 751 733 743 (24) 757 739 751 (22) 761 743 757 (26) 769 751 761 (22) 773 757 769 (30) 787 761 773 (36) 797 769 787 (40) 809 773 797 (38) 811 428 International Journal of Applied Mathematical Research 787 809 (34) 821 797 811 (26) 823 809 821 (18) 827 811 823 (18) 829 821 827 (18) 839 823 829 (20) 853 827 839 (30) 857 829 853 (30) 859 839 857 (24) 863 853 859 (24) 877 857 863 (24) 881 859 877 (24) 883 So on And so on for all prime number spirals, and a clear calculus to predict all prime number spiral values, based on this end calculus and what follows below .Most clearly the spirals are predictable and constant.