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数论小猜想

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发表于 2019-6-29 08:32 | 显示全部楼层
本帖最后由 白新岭 于 2019-6-29 01:39 编辑

113#的问题,对称4生素数(P,P+2,P+6,P+8),对称6生素数(P,P+4,P+6,P+10,P+12,P+16),和对称8生素数以外,其它对称2k生素数(以中心,向外以2^K为间距)都不一定是连续2k生素数,意思是说在它们之间有其它素数。
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发表于 2019-7-4 12:27 | 显示全部楼层
蔡家雄 发表于 2019-6-28 01:28
若 15x±2, 15x±2^2, 15x±2^3, ...... , 15x±2^n
是 对称2n生素数,n 可以任意大吗?

对于以中心为奇数的对称2n生素数,n可以任意大,因为它中的项模素数p皆剩余余数0不被占用,这是关键的,如果模素数p余数全部占用,则肯定没有这样的对称2n生素数,在公式求解中,这是最重要的一个条件,不过还有一个普通条件,那就是当素数值大于2n后,一定留有p-2n个余数类可以通过,之前可能去掉的余数类小于等于2n,但是最少保留1个剩余类。

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谢谢:白老师的分析!  发表于 2019-7-4 17:38
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 楼主| 发表于 2019-7-5 20:30 | 显示全部楼层
两相邻素数差==128 的相邻素数 有 无穷多个

1------3851587 - 3851459 = 128

2------9810781 - 9810653 = 128

3------11296801 - 11296673 = 128

4------13347031 - 13346903 = 128

5------16771609 - 16771481 = 128

6------22177081 - 22176953 = 128

7------24149941 - 24149813 = 128

8------29788699 - 29788571 = 128

9------34690291 - 34690163 = 128

10------36617407 - 36617279 = 128

11------37360621 - 37360493 = 128

12------37757767 - 37757639 = 128

13------38606467 - 38606339 = 128

14------38952607 - 38952479 = 128

15------42560647 - 42560519 = 128

16------43408411 - 43408283 = 128

17------43799941 - 43799813 = 128

18------45763777 - 45763649 = 128

19------46995079 - 46994951 = 128

20------48522337 - 48522209 = 128

21------49222339 - 49222211 = 128

22------51071611 - 51071483 = 128

23------51274381 - 51274253 = 128

24------52154437 - 52154309 = 128

25------52427857 - 52427729 = 128

26------52689937 - 52689809 = 128

27------53114251 - 53114123 = 128

28------53209111 - 53208983 = 128

29------56789101 - 56788973 = 128

30------59113111 - 59112983 = 128

31------60945301 - 60945173 = 128

32------63909187 - 63909059 = 128

33------65534239 - 65534111 = 128

34------65591161 - 65591033 = 128

35------65951311 - 65951183 = 128

36------66413287 - 66413159 = 128

37------69106447 - 69106319 = 128

38------69882151 - 69882023 = 128

39------70262977 - 70262849 = 128

40------70745137 - 70745009 = 128

41------70846879 - 70846751 = 128

42------71865841 - 71865713 = 128

43------72956659 - 72956531 = 128

44------74191279 - 74191151 = 128

45------74633917 - 74633789 = 128

46------75917131 - 75917003 = 128

47------76317781 - 76317653 = 128

48------76806031 - 76805903 = 128

49------77360581 - 77360453 = 128

50------77912449 - 77912321 = 128

51------77923357 - 77923229 = 128

52------78080797 - 78080669 = 128

53------79946299 - 79946171 = 128

54------80260177 - 80260049 = 128

55------81061681 - 81061553 = 128

56------81104377 - 81104249 = 128

57------83929789 - 83929661 = 128

58------84085321 - 84085193 = 128

59------87603367 - 87603239 = 128

60------87678067 - 87677939 = 128

61------88853119 - 88852991 = 128

62------90239581 - 90239453 = 128

63------90957187 - 90957059 = 128

64------92220577 - 92220449 = 128

65------92649721 - 92649593 = 128

66------93445867 - 93445739 = 128

67------94367617 - 94367489 = 128

68------94519897 - 94519769 = 128

69------95758027 - 95757899 = 128

70------96763657 - 96763529 = 128

71------97082809 - 97082681 = 128

72------97092001 - 97091873 = 128

73------97681951 - 97681823 = 128

74------98112997 - 98112869 = 128

75------98527537 - 98527409 = 128

76------99282889 - 99282761 = 128

77------101310889 - 101310761 = 128

78------102538651 - 102538523 = 128

79------104782801 - 104782673 = 128

80------105176917 - 105176789 = 128

81------105783661 - 105783533 = 128

82------107555431 - 107555303 = 128

83------108711727 - 108711599 = 128

84------109138957 - 109138829 = 128

85------109328917 - 109328789 = 128

86------110327311 - 110327183 = 128

87------110482429 - 110482301 = 128

88------111420817 - 111420689 = 128

89------111874201 - 111874073 = 128

90------111993949 - 111993821 = 128

91------112126057 - 112125929 = 128

92------112246237 - 112246109 = 128

93------113097451 - 113097323 = 128

94------113621941 - 113621813 = 128

95------114651127 - 114650999 = 128

96------116278021 - 116277893 = 128

97------118670089 - 118669961 = 128

98------119774701 - 119774573 = 128

99------119818861 - 119818733 = 128

100------120300127 - 120299999 = 128

101------120776587 - 120776459 = 128

102------121622341 - 121622213 = 128

103------122740099 - 122739971 = 128

104------123858937 - 123858809 = 128

105------124036291 - 124036163 = 128

106------124115137 - 124115009 = 128

107------124339279 - 124339151 = 128

108------124981111 - 124980983 = 128

109------126200317 - 126200189 = 128

110------126430417 - 126430289 = 128

111------126524371 - 126524243 = 128

112------127183501 - 127183373 = 128

113------128080921 - 128080793 = 128

114------128742151 - 128742023 = 128

115------129097627 - 129097499 = 128

116------129771877 - 129771749 = 128

117------130782271 - 130782143 = 128

118------131558407 - 131558279 = 128

119------131592187 - 131592059 = 128

120------133817407 - 133817279 = 128

121------135359017 - 135358889 = 128

122------135760021 - 135759893 = 128

123------135973741 - 135973613 = 128

124------136924471 - 136924343 = 128

125------137990059 - 137989931 = 128

126------139031107 - 139030979 = 128

127------139402177 - 139402049 = 128

128------139455541 - 139455413 = 128

129------139785901 - 139785773 = 128

130------140063851 - 140063723 = 128

131------140526739 - 140526611 = 128

132------140887051 - 140886923 = 128

133------141629311 - 141629183 = 128

134------141630889 - 141630761 = 128

135------146072767 - 146072639 = 128

136------146114671 - 146114543 = 128

137------146903161 - 146903033 = 128

138------147031501 - 147031373 = 128

139------148621651 - 148621523 = 128

140------148630081 - 148629953 = 128

141------148817707 - 148817579 = 128

142------150935287 - 150935159 = 128

143------151892497 - 151892369 = 128

144------153230641 - 153230513 = 128

145------153460051 - 153459923 = 128

146------153563521 - 153563393 = 128

147------153590659 - 153590531 = 128

148------153923827 - 153923699 = 128

149------157472977 - 157472849 = 128

150------157560187 - 157560059 = 128

151------157592401 - 157592273 = 128

152------158273119 - 158272991 = 128

153------158644039 - 158643911 = 128

154------158891881 - 158891753 = 128

155------159209467 - 159209339 = 128

156------159333607 - 159333479 = 128

157------161037211 - 161037083 = 128

158------162537829 - 162537701 = 128

159------163793137 - 163793009 = 128

160------164269291 - 164269163 = 128

161------164728339 - 164728211 = 128

162------164792347 - 164792219 = 128

163------165258817 - 165258689 = 128

164------165306391 - 165306263 = 128

165------166185559 - 166185431 = 128

166------166394467 - 166394339 = 128

167------166505959 - 166505831 = 128

168------167900521 - 167900393 = 128

169------167982469 - 167982341 = 128

170------168204937 - 168204809 = 128

171------168625591 - 168625463 = 128

172------170433829 - 170433701 = 128

173------170504377 - 170504249 = 128

174------171082447 - 171082319 = 128

175------171126679 - 171126551 = 128

176------171527479 - 171527351 = 128

177------172112557 - 172112429 = 128

178------172119121 - 172118993 = 128

179------172566829 - 172566701 = 128

180------176887177 - 176887049 = 128

181------178116877 - 178116749 = 128

182------178201951 - 178201823 = 128

183------178682701 - 178682573 = 128

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 楼主| 发表于 2019-7-6 06:42 | 显示全部楼层
相邻素数差==256 有 无穷多个

1------22884866957 - 22884866701 = 256

2------22983829217 - 22983828961 = 256

3------22985465813 - 22985465557 = 256

4------23006983679 - 23006983423 = 256

5------23030477819 - 23030477563 = 256

6------23031258119 - 23031257863 = 256

7------23298633557 - 23298633301 = 256

8------23451909749 - 23451909493 = 256

9------23532010757 - 23532010501 = 256

10------23630986007 - 23630985751 = 256

11------23648395937 - 23648395681 = 256

12------23795562377 - 23795562121 = 256

13------23824946603 - 23824946347 = 256

14------23866455443 - 23866455187 = 256

15------23946108539 - 23946108283 = 256

16------24017676737 - 24017676481 = 256

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发表于 2019-7-9 09:49 | 显示全部楼层
蔡家雄 发表于 2019-7-6 09:38
相邻素数差==16 有 无穷多个
最小解是:1------1847 - 1831 = 16,仅前10^7个素数,就有(多如牛毛)个相 ...

相邻素数差为2m的素数对是很少的,特别是大点的间距,比如1024的相邻素数对,出现范围就有点大了,就目前来说能找到相邻素数差为任意2m的素数对,中的2m有很多还是未找到的,最大的2m值也是非常小的。
所以,相邻这个条件是苛刻的。
不限制相邻,两个素数差的任意2m值都有无数组。比较有名气的就是孪生素数对猜想了。
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 楼主| 发表于 2019-7-10 13:59 | 显示全部楼层
10是如下 等差9生素数(公差9240)的原根,即:这些素数倒数具有最大循环节长!!!

1---(95339,104579,113819,123059,132299,141539,150779,160019,169259)

2---(7827167,7836407,7845647,7854887,7864127,7873367,7882607,7891847,7901087)

3---(9195167,9204407,9213647,9222887,9232127,9241367,9250607,9259847,9269087)

4---(32288903,32298143,32307383,32316623,32325863,32335103,32344343,32353583,32362823)

5---(59941697,59950937,59960177,59969417,59978657,59987897,59997137,60006377,60015617)

6---(72980177,72989417,72998657,73007897,73017137,73026377,73035617,73044857,73054097)

7---(77003567,77012807,77022047,77031287,77040527,77049767,77059007,77068247,77077487)

8---(121526753,121535993,121545233,121554473,121563713,121572953,121582193,121591433,121600673)

9---(121535993,121545233,121554473,121563713,121572953,121582193,121591433,121600673,121609913)

10---(171184589,171193829,171203069,171212309,171221549,171230789,171240029,171249269,171258509)

11---(194416847,194426087,194435327,194444567,194453807,194463047,194472287,194481527,194490767)

12---(216760967,216770207,216779447,216788687,216797927,216807167,216816407,216825647,216834887)

13---(216770207,216779447,216788687,216797927,216807167,216816407,216825647,216834887,216844127)

14---(216779447,216788687,216797927,216807167,216816407,216825647,216834887,216844127,216853367)

15---(229140029,229149269,229158509,229167749,229176989,229186229,229195469,229204709,229213949)

16---(242125979,242135219,242144459,242153699,242162939,242172179,242181419,242190659,242199899)

17---(258061109,258070349,258079589,258088829,258098069,258107309,258116549,258125789,258135029)

18---(340517447,340526687,340535927,340545167,340554407,340563647,340572887,340582127,340591367)

19---(340526687,340535927,340545167,340554407,340563647,340572887,340582127,340591367,340600607)

20---(340535927,340545167,340554407,340563647,340572887,340582127,340591367,340600607,340609847)

21---(491843873,491853113,491862353,491871593,491880833,491890073,491899313,491908553,491917793)

22---(572317847,572327087,572336327,572345567,572354807,572364047,572373287,572382527,572391767)

23---(598443353,598452593,598461833,598471073,598480313,598489553,598498793,598508033,598517273)

24---(719978783,719988023,719997263,720006503,720015743,720024983,720034223,720043463,720052703)

25---(789954829,789964069,789973309,789982549,789991789,790001029,790010269,790019509,790028749)

26---(950955623,950964863,950974103,950983343,950992583,951001823,951011063,951020303,951029543)

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 楼主| 发表于 2019-7-10 15:26 | 显示全部楼层
等差13生素数(公差2*3*5*7*11*13)

1---(14933623,14963653,14993683,15023713,15053743,15083773,15113803,15143833,15173863,15203893,15233923,15263953,15293983)
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发表于 2019-7-12 16:59 | 显示全部楼层
等差k生素数多如牛毛,公差越大(不同因子组成,排除相同因子),则数量越多,比起最密k生素数要多的多。
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 楼主| 发表于 2019-7-18 18:18 | 显示全部楼层
白老师:素数差成等比的10生素数:

p,p+6*1,p+6*3,p+6*7,p+6*15,p+6*31,p+6*63,p+6*127,p+6*255,p+6*511,
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发表于 2019-7-18 19:27 | 显示全部楼层
蔡家雄 发表于 2019-7-18 10:18
白老师:素数差成等比的10生素数:

p,p+6*1,p+6*3,p+6*7,p+6*15,p+6*31,p+6*63,p+6*127,p+6*255,p+6*511 ...

的确构造了一组10生素数的素数差为等比数列,我看一看它的存在性,如果存在我会给出系数和数量。
稍等........,很快就有结果了。
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