HOME plateWON | World!OfNumbers Near Smoothly Undulating Primes (NSUP's)  (with 6-digit undulators) 1   2   3   4   5   6  Near Smoothly Undulating Primes NSUP's (with 22-digit undulators) Undulating Palindromic Primes Palindromic Wing Primes Plateau & Depression Palindromic Primes Palindromic Merlon Primes Home Primes Circular Primes SUPP-sorted

NSUP” Prime Projects

Hereunder at the left you'll find the table with files containing the primefactors of the SUPP's (Smoothly Undulating Palindromic Primes).
At the right you'll find the corresponding 6-digit NSUP's.

Case [k](d1d2d3d4d5d6)u = [prefix](6-digit undulator).
Attentive readers of the factor lists will have noticed with me that some SUPP primefactors are themselves near smoothly undulating. 'Near' because of an initial prefix and the repeating 6-digit undulators.
We divide therefore the SUPP by primefactor 3 (see table 'Mark 3') or 7 (see table 'Mark 7').

Hereunder at the left you'll find the table with the files containing the primefactors of the SUP's (Smoothly Undulating Palindromes).
At the right you'll find the corresponding 6-digit NSUP's.

Case [k](d1d2d3d4d5d6)u = [prefix](6-digit undulator).
Attentive readers of the factor lists will have noticed with me that some SUP primefactors are themselves near smoothly undulating. 'Near' because of an initial prefix and the repeating 6-digit undulators.
We divide therefore the SUP by a power of 2 or a power of 5 and the primefactor 3 (see table 'Mark 3').

 SUP (Smoothly Undulating Composite Palindromes) reference files 2(12)w = (21*10n–12)/99 facsup212.htm (by P. De Geest). 2(32)w = (23*10n–32)/99 facsup232.htm (by P. De Geest). 2(52)w = (25*10n–52)/99 facsup252.htm (by P. De Geest). 2(72)w = (27*10n–72)/99 facsup272.htm (by P. De Geest). 2(92)w = (29*10n–92)/99 facsup292.htm (by P. De Geest). 4(14)w = (41*10n–14)/99 facsup414.htm (by P. De Geest). 4(34)w = (43*10n–34)/99 facsup434.htm (by P. De Geest). 4(54)w = (45*10n–54)/99 facsup454.htm (by P. De Geest). 4(74)w = (47*10n–74)/99 facsup474.htm (by P. De Geest). 4(94)w = (49*10n–94)/99 facsup494.htm (by P. De Geest). 5(15)w = (51*10n–15)/99 facsup515.htm (by P. De Geest). 5(25)w = (52*10n–25)/99 facsup525.htm (by P. De Geest). 5(35)w = (53*10n–35)/99 facsup535.htm (by P. De Geest). 5(45)w = (54*10n–45)/99 facsup545.htm (by P. De Geest). 5(65)w = (56*10n–65)/99 facsup565.htm (by P. De Geest). 5(75)w = (57*10n–75)/99 facsup575.htm (by P. De Geest). 5(85)w = (58*10n–85)/99 facsup585.htm (by P. De Geest). 5(95)w = (59*10n–95)/99 facsup595.htm (by P. De Geest). 6(16)w = (61*10n–16)/99 facsup616.htm (by P. De Geest). 6(56)w = (65*10n–56)/99 facsup656.htm (by P. De Geest). 6(76)w = (67*10n–76)/99 facsup676.htm (by P. De Geest). 7(67)w = (76*10n–67)/99 facsup767.htm (by P. De Geest). 8(18)w = (81*10n–18)/99 facsup818.htm (by P. De Geest). 8(38)w = (83*10n–38)/99 facsup838.htm (by P. De Geest). 8(58)w = (85*10n–58)/99 facsup858.htm (by P. De Geest). 8(78)w = (87*10n–78)/99 facsup878.htm (by P. De Geest). 8(98)w = (89*10n–98)/99 facsup898.htm (by P. De Geest).

Case [k](d1d2d3d4d5d6)u = [prefix](6-digit undulator).
Attentive readers of the factor lists will have noticed with me that some SUP primefactors are themselves near smoothly undulating. 'Near' because of an initial prefix and the repeating 6-digit undulators.
This time we divide the SUP with some or all of its prime factors upto 13. The number of candidates for 'Mark 13' are significant lower than the previous ones (only 5 cases found) hence the following concise table.
'Mark 11' wasn't forgotten but yield only 22-digit undulators (For these cases with long undulators see undulmore.htm).

 [k](d1d2d3d4d5d6)n = NSUP's (Near Smoothly Undulating Primes) Mark 13 4(94)w / 2 / 13 (49*10n–94)/(99*2*13) = [19](036519)u Step 6w + 3 Link 5(85)w / 3 / 5 / 13 (58*10n–85)/(99*3*5*13) = [3](004403)u Step 6w + 3 Link 6(76)w / 22 / 13 (67*10n–76)/(99*4*13) = [13](014763)u Step 6w + 3 Link 7(67)w / 13 (76*10n–67)/(99*13) = [59](052059)u Step 6w + 3 Link 8(58)w / 2 / 3 / 13 (85*10n–58)/(99*2*3*13) = [11](007511)u Step 6w + 3 Link
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The “NSUP” Table

 The reference table forNear Smoothly Undulating PrimesCases with 6-digit undulatorsderived from the SUPP's Mark 3 This collection is complete forprobable primes up to see headings digits. `PDG = Patrick De Geest` NSUP FormulaAccolades = prime exp Who When Status PrimeCertificat ¬ n ⩾ 50141 (PDG, August 16, 2022) 1(31)2498/3 = [4377](104377)832 (13*104997–31)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 50655 (PDG, August 16, 2022) 1(41)1/3 = [47](138047)0 (14*10{3}–41)/(99*3) PDG Aug 06 2022 PRP View 1(41)199/3 = [47](138047)66 (14*10399–41)/(99*3) PDG Aug 06 2022 PRP View 1(41)16654/3 = [47](138047)5551 (14*1033309–41)/(99*3) PDG Aug 16 2022 PRP View ¬ n ⩾ 51677 (PDG, August 17, 2022) 1(61)2/3 = [5387](205387)0 (16*10{5}–61)/(99*3) PDG Aug 06 2022 PRP View 1(61)206/3 = [5387](205387)68 (16*10413–61)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 50001 (PDG, August 7, 2022) 1(71)85/3 = [57](239057)28 (17*10171–71)/(99*3) PDG Aug 06 2022 PRP View 1(71)202/3 = [57](239057)67 (17*10405–71)/(99*3) PDG Aug 06 2022 PRP View 1(71)526/3 = [57](239057)175 (17*101053–71)/(99*3) PDG Aug 06 2022 PRP View 1(71)4777/3 = [57](239057)1592 (17*109555–71)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 50009 (PDG, August 7, 2022) 1(91)2/3 = [6397](306397)0 (19*10{5}–91)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 50095 (PDG, August 17, 2022) 3(13)57/3 = [1](043771)19 (31*10115–13)/(99*3) PDG Aug 06 2022 PRP View 3(13)381/3 = [1](043771)127 (31*10763–13)/(99*3) PDG Aug 06 2022 PRP View 3(13)2610/3 = [1](043771)870 (31*105221–13)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 50161 (PDG, August 17, 2022) 3(23)132/3 = [1](077441)44 (32*10265–23)/(99*3) PDG Aug 06 2022 PRP View 3(23)4050/3 = [1](077441)1350 (32*10{8101}–23)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 51433 (PDG, August 17, 2022) 3(43)255/3 = [1](144781)85 (34*10511–43)/(99*3) PDG Aug 06 2022 PRP View 3(43)16995/3 = [1](144781)5665 (34*1033991–43)/(99*3) PDG Aug 17 2022 PRP View 3(43)21198/3 = [1](144781)7066 (34*10{42397}–43)/(99*3) PDG Aug 17 2022 PRP View ¬ n ⩾ 51997 (PDG, August 17, 2022) 3(53)6/3 = [1](178451)2 (35*10{13}–53)/(99*3) PDG Aug 06 2022 PRP View 3(53)15/3 = [1](178451)5 (35*10{31}–53)/(99*3) PDG Aug 06 2022 PRP View 3(53)87/3 = [1](178451)29 (35*10175–53)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 50101 (PDG, August 17, 2022) 3(73)3/3 = [1](245791)1 (37*10{7}–73)/(99*3) PDG Aug 06 2022 PRP View 3(73)12/3 = [1](245791)4 (37*1025–73)/(99*3) PDG Aug 06 2022 PRP View 3(73)435/3 = [1](245791)145 (37*10871–73)/(99*3) PDG Aug 06 2022 PRP View 3(73)462/3 = [1](245791)154 (37*10925–73)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 53689 (PDG, August 18, 2022) 3(83)6/3 = [1](279461)2 (38*10{13}–83)/(99*3) PDG Aug 06 2022 PRP View 3(83)33/3 = [1](279461)11 (38*10{67}–83)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 53001 (PDG, August 18, 2022) 7(17)1/3 = [239](057239)0 (71*10{3}–17)/(99*3) PDG Aug 06 2022 PRP View 7(17)4141/3 = [239](057239)1380 (71*108283–17)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 50231 (PDG, August 18, 2022) 7(37)26/3 = [24579](124579)8 (73*10{53}–37)/(99*3) PDG Aug 06 2022 PRP View 7(37)20771/3 = [24579](124579)6923 (73*10{41543}–37)/(99*3) PDG Aug 18 2022 PRP View ¬ n ⩾ 51705 (PDG, August 18, 2022) 7(47)7/3 = [24579](124579)2 (74*1015–47)/(99*3) PDG Aug 06 2022 PRP View 7(47)5137/3 = [24579](124579)1712 (74*1010275–47)/(99*3) PDG Aug 06 2022 PRP View 7(47)5188/3 = [24579](124579)1729 (74*1010377–47)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 50315 (PDG, August 19, 2022) 7(97)1361/3 = [26599](326599)453 (79*102723–97)/(99*3) PDG Aug 06 2022 PRP View 7(97)11714/3 = [26599](326599)3904 (79*1023429–97)/(99*3) PDG Aug 19 2022 PRP View 7(97)16706/3 = [26599](326599)5568 (79*10{33413}–97)/(99*3) PDG Aug 19 2022 PRP View ¬ n ⩾ 50353 (PDG, August 19, 2022) 9(19)0/3 = [3](063973)0 (91*101–19)/(99*3) PDG Aug 06 2022 PRP View 9(19)2748/3 = [3](063973)916 (91*105497–19)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 51289 (PDG, August 19, 2022) 9(29)0/3 = [3](097643)0 (92*101–29)/(99*3) PDG Aug 06 2022 PRP View 9(29)141/3 = [3](097643)47 (92*10{283}–29)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 50071 (PDG, August 19, 2022) 9(49)0/3 = [3](164983)0 (94*101–49)/(99*3) PDG Aug 06 2022 PRP View 9(49)3/3 = [3](164983)1 (94*10{7}–49)/(99*3) PDG Aug 06 2022 PRP View 9(49)5547/3 = [3](164983)1849 (94*1011095–49)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 58615 (PDG, August 20, 2022) 9(59)0/3 = [3](198653)0 (95*101–59)/(99*3) PDG Aug 06 2022 PRP View 9(59)3/3 = [3](198653)1 (95*10{7}–59)/(99*3) PDG Aug 06 2022 PRP View 9(59)12/3 = [3](198653)4 (95*1025–59)/(99*3) PDG Aug 06 2022 PRP View 9(59)84/3 = [3](198653)28 (95*10169–59)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 52375 (PDG, August 20, 2022) 9(79)0/3 = [3](265993)0 (97*101–79)/(99*3) PDG Aug 06 2022 PRP View 9(79)3/3 = [3](265993)1 (97*10{7}–79)/(99*3) PDG Aug 06 2022 PRP View 9(79)24/3 = [3](265993)8 (97*1049–79)/(99*3) PDG Aug 06 2022 PRP View 9(79)42/3 = [3](265993)14 (97*1085–79)/(99*3) PDG Aug 06 2022 PRP View 9(79)1023/3 = [3](265993)341 (97*102047–79)/(99*3) PDG Aug 06 2022 PRP View 9(79)2040/3 = [3](265993)680 (97*104081–79)/(99*3) PDG Aug 06 2022 PRP View ¬ n ⩾ 51079 (PDG, August 20, 2022) 9(89)0/3 = [3](299663)0 (98*101–89)/(99*3) PDG Aug 06 2022 PRP View 9(89)6/3 = [3](299663)2 (98*10{13}–89)/(99*3) PDG Aug 06 2022 PRP View 9(89)975/3 = [3](299663)325 (98*10{1951}–89)/(99*3) PDG Aug 06 2022 PRP View

 The reference table forNear Smoothly Undulating PrimesCases with 6-digit undulatorsderived from the composite set of SUP's Mark 3 This collection is complete forprobable primes up to see headings digits. `PDG = Patrick De Geest` NSUP FormulaAccolades = prime exp Who When Status PrimeCertificat ¬ n ⩾ 53855 (PDG, August 21, 2022) 2(32)4706/25/3 = [242](003367)1568 (23*10{9413}–32)/(99*32*3) PDG Aug 09 2022 PRP View ¬ n ⩾ 50063 (PDG, August 21, 2022) 2(92)2/22/3 = [2441](077441)0 (29*10{5}–92)/(99*4*3) PDG Aug 09 2022 PRP View ¬ n ⩾ 50067 (PDG, August 21, 2022) 4(14)7/2/3 = [69](023569)2 (41*1015–14)/(99*2*3) PDG Aug 09 2022 PRP View 4(14)250/2/3 = [69](023569)83 (41*10501–14)/(99*2*3) PDG Aug 09 2022 PRP View 4(14)2676/2/3 = [69](023569)890 (41*105343–14)/(99*2*3) PDG Aug 09 2022 PRP View ¬ n ⩾ 72305 (PDG, August 21, 2022) 4(34)143/2/3 = [7239](057239)47 (43*10287–34)/(99*2*3) PDG Aug 09 2022 PRP View 4(34)7109/2/3 = [7239](057239)2369 (43*1014219–34)/(99*2*3) PDG Aug 09 2022 PRP View ¬ n ⩾ 53325 (PDG, August 22, 2022) 4(74)1/2/3 = [79](124579)0 (47*10{3}–74)/(99*2*3) PDG Aug 09 2022 PRP View 4(74)226/2/3 = [79](124579)75 (47*10453–74)/(99*2*3) PDG Aug 09 2022 PRP View ¬ n ⩾ 52259 (PDG, August 22, 2022) 4(94)59/2/3 = [8249](158249)19 (49*10119–94)/(99*2*3) PDG Aug 09 2022 PRP View ¬ n ⩾ 50729 (PDG, August 10, 2022) 5(35)35/5/3 = [3569](023569)11 (53*10{71}–35)/(99*5*3) PDG Aug 09 2022 PRP View 5(35)218/5/3 = [3569](023569)72 (53*10437–35)/(99*5*3) PDG Aug 09 2022 PRP View ¬ n ⩾ 50609 (PDG, August 22, 2022) 5(65)32/5/3 = [3771](043771)10 (56*1065–65)/(99*5*3) PDG Aug 09 2022 PRP View 5(65)1646/5/3 = [3771](043771)548 (56*103293–65)/(99*5*3) PDG Aug 09 2022 PRP View ¬ n ⩾ 67655 (PDG, August 23, 2022) 5(95)20/5/3 = [3973](063973)6 (59*10{41}–95)/(99*5*3) PDG Aug 09 2022 PRP View 5(95)695/5/3 = [3973](063973)231 (59*101391–95)/(99*5*3) PDG Aug 09 2022 PRP View ¬ n ⩾ 80047 (PDG, August 12, 2022) 6(16)?/24/3 = [128367](003367)? (61*10?–16)/(99*16*3) PDG Aug 11 2022 PRP View ¬ n ⩾ 65935 (PDG, August 23, 2022) 6(56)3/23/3 = [273569](023569)0 (65*10{7}–56)/(99*8*3) PDG Aug 11 2022 PRP View 6(56)7425/23/3 = [273569](023569)2474 (65*10{14851}–56)/(99*8*3) PDG Aug 11 2022 PRP View ¬ n ⩾ 50035 (PDG, August 11, 2022) 6(76)9/22/3 = [563973](063973)2474 (67*10{19}–76)/(99*4*3) PDG Aug 11 2022 PRP View 6(76)11979/22/3 = [563973](063973)3992 (67*1023959–76)/(99*4*3) PDG Aug 11 2022 PRP View ¬ n ⩾ 53951 (PDG, August 23, 2022) 7(67)2/3 = [25589](225589)0 (76*10{5}–67)/(99*3) PDG Aug 11 2022 PRP View 7(67)29/3 = [25589](225589)9 (76*10{59}–67)/(99*3) PDG Aug 11 2022 PRP View ¬ n ⩾ 53213 (PDG, August 24, 2022) 8(38)11/2/3 = [13973](063973)3 (83*10{23}–38)/(99*2*3) PDG Aug 11 2022 PRP View 8(38)107/2/3 = [13973](063973)35 (83*10215–38)/(99*2*3) PDG Aug 11 2022 PRP View 8(38)161/2/3 = [13973](063973)53 (83*10323–38)/(99*2*3) PDG Aug 11 2022 PRP View 8(38)389/2/3 = [13973](063973)129 (83*10779–38)/(99*2*3) PDG Aug 11 2022 PRP View ¬ n ⩾ 52385 (PDG, August 24, 2022) 8(98)2/2/3 = [14983](164983)0 (89*10{5}–98)/(99*2*3) PDG Aug 11 2022 PRP View 8(98)3218/2/3 = [14983](164983)1072 (89*10{6437}–98)/(99*2*3) PDG Aug 11 2022 PRP View

 The reference table forNear Smoothly Undulating PrimesCases with 6-digit undulatorsderived from the composite set of SUPP's Mark 7 This collection is complete forprobable primes up to see headings digits. `PDG = Patrick De Geest` NSUP FormulaAccolades = prime exp Who When Status PrimeCertificat ¬ n ⩾ 51003 (PDG, August 24, 2022) 1(61)40/7 = [23](088023)13 (16*1081–61)/(99*7) PDG Aug 12 2022 PRP View 1(61)160/7 = [23](088023)53 (16*10321–61)/(99*7) PDG Aug 12 2022 PRP View 1(61)190/7 = [23](088023)63 (16*10381–61)/(99*7) PDG Aug 12 2022 PRP View 1(61)442/7 = [23](088023)147 (16*10885–61)/(99*7) PDG Aug 12 2022 PRP View 1(61)511/7 = [23](088023)170 (16*101023–61)/(99*7) PDG Aug 12 2022 PRP View ¬ n ⩾ 51359 (PDG, August 12, 2022) 1(71)?/7 = [2453](102453)? (17*10?–71)/(99*7) PDG Aug 12 2022 PRP View ¬ n ⩾ 50031 (PDG, August 25, 2022) 3(43)79/7 = [49](062049)26 (34*10159–43)/(99*7) PDG Aug 12 2022 PRP View 3(43)2809/7 = [49](062049)936 (34*105619–43)/(99*7) PDG Aug 12 2022 PRP View ¬ n ⩾ 54083 (PDG, August 12, 2022) 3(73)1230/7 = [5339](105339)410 (37*102465–73)/(99*7) PDG Aug 12 2022 PRP View ¬ n ⩾ 52381 (PDG, August 25, 2022) 7(17)21/7 = [1](024531)7 (71*10{43}–17)/(99*7) PDG Aug 12 2022 PRP View 7(17)24/7 = [1](024531)8 (71*1049–17)/(99*7) PDG Aug 12 2022 PRP View ¬ n ⩾ 53947 (PDG, August 25, 2022) 7(27)9/7 = [1](038961)3 (72*10{19}–27)/(99*7) PDG Aug 12 2022 PRP View 7(27)33/7 = [1](038961)11 (72*10{67}–27)/(99*7) PDG Aug 12 2022 PRP View 7(27)84/7 = [1](038961)28 (72*10169–27)/(99*7) PDG Aug 12 2022 PRP View 7(27)114/7 = [1](038961)38 (72*10{229}–27)/(99*7) PDG Aug 12 2022 PRP View 7(27)180/7 = [1](038961)60 (72*10361–27)/(99*7) PDG Aug 12 2022 PRP View 7(27)10851/7 = [1](038961)3617 (72*1021703–27)/(99*7) PDG Aug 12 2022 PRP View ¬ n ⩾ 51139 (PDG, August 26, 2022) 7(37)?/7 = [1](053391)? (73*10?–37)/(99*7) PDG Aug 13 2022 PRP View ¬ n ⩾ 50473 (PDG, August 26, 2022) 7(47)6/7 = [1](067821)2 (74*10{13}–47)/(99*7) PDG Aug 13 2022 PRP View 7(47)9/7 = [1](067821)3 (74*10{19}–47)/(99*7) PDG Aug 13 2022 PRP View 7(47)183/7 = [1](067821)61 (74*10{367}–47)/(99*7) PDG Aug 13 2022 PRP View ¬ n ⩾ 54451 (PDG, August 26, 2022) 7(57)2760/7 = [1](082251)920 (75*10{5521}–57)/(99*7) PDG Aug 13 2022 PRP View 7(57)5904/7 = [1](082251)1968 (75*1011809–57)/(99*7) PDG Aug 13 2022 PRP View ¬ n ⩾ 54901 (PDG, August 27, 2022) 7(87)9/7 = [1](125541)3 (78*10{19}–87)/(99*7) PDG Aug 13 2022 PRP View 7(87)600/7 = [1](125541)200 (78*10{1201}–87)/(99*7) PDG Aug 13 2022 PRP View 7(87)1509/7 = [1](125541)503 (78*10{3019}–87)/(99*7) PDG Aug 13 2022 PRP View ¬ n ⩾ 53881 (PDG, August 27, 2022) 7(97)12/7 = [1](139971)4 (79*1025–97)/(99*7) PDG Aug 13 2022 PRP View 7(97)6438/7 = [1](139971)2146 (79*1012877–97)/(99*7) PDG Aug 13 2022 PRP View ¬ n ⩾ 52167 (PDG, August 27, 2022) 9(59)7/7 = [137](085137)2 (95*1015–59)/(99*7) PDG Aug 13 2022 PRP View 9(59)79/7 = [137](085137)26 (95*10159–59)/(99*7) PDG Aug 13 2022 PRP View 9(59)202/7 = [137](085137)67 (95*10405–59)/(99*7) PDG Aug 13 2022 PRP View 9(59)7924/7 = [137](085137)2641 (95*1015849–59)/(99*7) PDG Aug 13 2022 PRP View ¬ n ⩾ 50189 (PDG, August 27, 2022) 9(79)2/7 = [13997](113997)0 (97*10{5}–79)/(99*7) PDG Aug 13 2022 PRP View 9(79)8/7 = [13997](113997)2 (97*10{17}–79)/(99*7) PDG Aug 13 2022 PRP View 9(79)3782/7 = [13997](113997)1260 (97*107565–79)/(99*7) PDG Aug 13 2022 PRP View 9(79)5321/7 = [13997](113997)1773 (97*1010643–79)/(99*7) PDG Aug 13 2022 PRP View

 The reference table forNear Smoothly Undulating PrimesCases with 6-digit undulatorsderived from the composite set of SUP's Mark 7 This collection is complete forprobable primes up to see headings digits. `PDG = Patrick De Geest` NSUP FormulaAccolades = prime exp Who When Status PrimeCertificat ¬ n ⩾ 54015 (PDG, August 27, 2022) 2(52)1/4/3/7 = [3](006253)0 (25*10{3}–52)/(99*4*3*7) PDG Aug 14 2022 PRP View 2(52)1726/4/3/7 = [3](006253)575 (25*103453–52)/(99*4*3*7) PDG Aug 14 2022 PRP View ¬ n ⩾ 55145 (PDG, August 27, 2022) 2(72)2/23/7 = [487](012987)0 (27*10{5}–72)/(99*8*7) PDG Aug 14 2022 PRP View 2(72)32/23/7 = [487](012987)10 (27*1065–72)/(99*8*7) PDG Aug 14 2022 PRP View 2(72)440/23/7 = [487](012987)146 (27*10{881}–72)/(99*8*7) PDG Aug 14 2022 PRP View 2(72)1328/23/7 = [487](012987)442 (27*10{2657}–72)/(99*8*7) PDG Aug 14 2022 PRP View ¬ n ⩾ 51465 (PDG, August 28, 2022) 4(34)1/2/7 = [31](024531)0 (43*10{3}–34)/(99*2*7) PDG Aug 14 2022 PRP View 4(34)4/2/7 = [31](024531)45 (43*109–34)/(99*2*7) PDG Aug 14 2022 PRP View 4(34)22/2/7 = [31](024531)7 (43*1045–34)/(99*2*7) PDG Aug 14 2022 PRP View 4(34)43/2/7 = [31](024531)14 (43*1087–34)/(99*2*7) PDG Aug 14 2022 PRP View 4(34)193/2/7 = [31](024531)64 (43*10387–34)/(99*2*7) PDG Aug 14 2022 PRP View 4(34)6670/2/7 = [31](024531)2223 (43*1013341–34)/(99*2*7) PDG Aug 14 2022 PRP View ¬ n ⩾ 53261 (PDG, August 28, 2022) 4(74)2/2/7 = [3391](053391)0 (47*10{5}–74)/(99*2*7) PDG Aug 14 2022 PRP View 4(74)11/2/7 = [3391](053391)3 (47*10{23}–74)/(99*2*7) PDG Aug 14 2022 PRP View 4(74)41/2/7 = [3391](053391)13 (47*10{83}–74)/(99*2*7) PDG Aug 14 2022 PRP View 4(74)224/2/7 = [3391](053391)74 (47*10{449}–74)/(99*2*7) PDG Aug 14 2022 PRP View 4(74)1637/2/7 = [3391](053391)545 (47*103275–74)/(99*2*7) PDG Aug 14 2022 PRP View ¬ n ⩾ 51195 (PDG, August 28, 2022) 5(25)1/52/3/7 = [1](000481)0 (52*10{3}–25)/(99*25*3*7) PDG Aug 14 2022 PRP View 5(25)10/52/3/7 = [1](000481)3 (52*1021–25)/(99*25*3*7) PDG Aug 14 2022 PRP View 5(25)40/52/3/7 = [1](000481)13 (52*1081–25)/(99*25*3*7) PDG Aug 14 2022 PRP View 5(25)21964/52/3/7 = [1](000481)7321 (52*1043929–25)/(99*25*3*7) PDG Aug 28 2022 PRP View ¬ n ⩾ 51677 (PDG, August 28, 2022) 5(75)11/52/7 = [329](004329)3 (57*10{23}–75)/(99*25*7) PDG Aug 14 2022 PRP View 5(75)26/52/7 = [329](004329)8 (57*10{53}–75)/(99*25*7) PDG Aug 14 2022 PRP View 5(75)428/52/7 = [329](004329)142 (57*10{857}–75)/(99*25*7) PDG Aug 14 2022 PRP View 5(75)644/52/7 = [329](004329)214 (57*10{1289}–75)/(99*25*7) PDG Aug 28 2022 PRP View ¬ n ⩾ 50127 (PDG, August 28, 2022) 5(95)1/5/7 = [17](027417)0 (59*10{3}–95)/(99*5*7) PDG Aug 14 2022 PRP View 5(95)232/5/7 = [17](027417)77 (59*10465–95)/(99*5*7) PDG Aug 14 2022 PRP View 5(95)3391/5/7 = [17](027417)1130 (59*106783–95)/(99*5*7) PDG Aug 14 2022 PRP View 5(95)20791/5/7 = [17](027417)6930 (59*1041583–95)/(99*5*7) PDG Aug 28 2022 PRP View ¬ n ⩾ 52089 (PDG, August 28, 2022) 6(16)4/24/7 = [5501443](001443)0 (61*109–16)/(99*16*7) PDG Aug 15 2022 PRP View 6(16)10/24/7 = [5501443](001443)2 (61*1021–16)/(99*16*7) PDG Aug 15 2022 PRP View ¬ n ⩾ 51365 (PDG, August 29, 2022) 6(76)2/22/7 = [2417](027417)0 (67*10{5}–76)/(99*4*7) PDG Aug 15 2022 PRP View 6(76)8/22/7 = [2417](027417)2 (67*10{17}–76)/(99*4*7) PDG Aug 15 2022 PRP View 6(76)134/22/7 = [2417](027417)44 (67*10{269}–76)/(99*4*7) PDG Aug 15 2022 PRP View 6(76)17123/22/7 = [2417](027417)5707 (67*1034247–76)/(99*4*7) PDG Aug 29 2022 PRP View ¬ n ⩾ 52915 (PDG, August 29, 2022) 7(67)84/7 = [1](096681)28 (76*10169–67)/(99*7) PDG Aug 15 2022 PRP View 7(67)1035/7 = [1](096681)345 (76*102071–67)/(99*7) PDG Aug 15 2022 PRP View 7(67)8670/7 = [1](096681)2890 (76*1017341–67)/(99*7) PDG Aug 15 2022 PRP View ¬ n ⩾ 60029 (PDG, August 16, 2022) 8(78)2/2/7 = [6277](056277)0 (87*10{5}–78)/(99*2*7) PDG Aug 15 2022 PRP View

 The reference table forNear Smoothly Undulating PrimesCases with 6-digit undulatorsderived from both sets of SUPP's and SUP's Mark 13 This collection is complete forprobable primes up to see headings digits. `PDG = Patrick De Geest` NSUP FormulaAccolades = prime exp Who When Status PrimeCertificat ¬ n ⩾ 20175 (PDG, August 25, 2022) 4(94)1/2/13 = [19](036519)0 (49*10{3}–94)/(99*2*13) PDG Aug 24 2022 PRP View 4(94)4/2/13 = [19](036519)1 (49*109–94)/(99*2*13) PDG Aug 24 2022 PRP View 4(94)76/2/13 = [19](036519)25 (49*10153–94)/(99*2*13) PDG Aug 24 2022 PRP View ¬ n ⩾ 20427 (PDG, August 25, 2022) 5(85)1/3/5/13 = [3](004403)0 (58*10{3}–58)/(99*3*5*13) PDG Aug 24 2022 PRP View 5(85)4/3/5/13 = [3](004403)1 (58*109–58)/(99*3*5*13) PDG Aug 24 2022 PRP View 5(85)7/3/5/13 = [3](004403)2 (58*1015–58)/(99*3*5*13) PDG Aug 24 2022 PRP View 5(85)358/3/5/13 = [3](004403)119 (58*10717–58)/(99*3*5*13) PDG Aug 24 2022 PRP View 5(85)1204/3/5/13 = [3](004403)401 (58*102409–58)/(99*3*5*13) PDG Aug 24 2022 PRP View ¬ n ⩾ 20259 (PDG, August 25, 2022) 6(76)1/22/13 = [13](014763)0 (67*10{3}–76)/(99*4*13) PDG Aug 24 2022 PRP View 6(76)4/22/13 = [13](014763)1 (67*109–76)/(99*4*13) PDG Aug 24 2022 PRP View 6(76)10/22/13 = [13](014763)3 (67*1021–76)/(99*4*13) PDG Aug 24 2022 PRP View 6(76)178/22/13 = [13](014763)59 (67*10357–76)/(99*4*13) PDG Aug 24 2022 PRP View 6(76)580/22/13 = [13](014763)193 (67*101161–76)/(99*4*13) PDG Aug 24 2022 PRP View 6(76)2851/22/13 = [13](014763)950 (67*105703–76)/(99*4*13) PDG Aug 24 2022 PRP View ¬ n ⩾ 20109 (PDG, August 25, 2022) 7(67)1/13 = [59](052059)0 (76*10{3}–67)/(99*13) PDG Aug 24 2022 PRP View 7(67)13/13 = [59](052059)4 (76*1027–67)/(99*13) PDG Aug 24 2022 PRP View 7(67)34/13 = [59](052059)11 (76*1069–67)/(99*13) PDG Aug 24 2022 PRP View 7(67)604/13 = [59](052059)201 (76*101209–67)/(99*13) PDG Aug 24 2022 PRP View 7(67)718/13 = [59](052059)239 (76*101437–67)/(99*13) PDG Aug 24 2022 PRP View 7(67)874/13 = [59](052059)291 (76*101749–67)/(99*13) PDG Aug 24 2022 PRP View ¬ n ⩾ 40035 (PDG, August 25, 2022) 8(58)1/2/3/13 = [11](007511)0 (85*10{3}–58)/(99*2*3*13) PDG Aug 24 2022 PRP View 8(58)10/2/3/13 = [11](007511)3 (85*1021–58)/(99*2*3*13) PDG Aug 24 2022 PRP View 8(58)13/2/3/13 = [11](007511)4 (85*1027–58)/(99*2*3*13) PDG Aug 24 2022 PRP View 8(58)12703/2/3/13 = [11](007511)4234 (85*1025407–58)/(99*2*3*13) PDG Aug 25 2022 PRP View

Sources Revealed

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