制作等式队列的素材：部分回文数的质因数分解

记F₁(m)≡10^m+1＋1＝100…01 (中间m个0)

（m＝1，2，3，……，下同）

F₁(1)＝101质数

F₁(2)＝1001＝7×11×13

F₁(3 )＝10001＝73×137

F₁(4)＝100001＝11×9091

F₁ (5 )＝1000001＝101×9901

F₁ (6)＝10000001＝11×909091

F₁ (7 )＝100000001＝17×5882353

F₁ (8 )＝1000000001＝7×11×13×19×52579

F₁ (9)＝10000000001＝101×3541×27961

F₁ (10 )＝100000000001＝11²×23×4093×8779

F₁ (11)＝1000000000001＝73×137×99990001

F₁ (12)＝10000000000001＝11×859×1058313049

F₁ (13)＝100000000000001＝29×101×281×121499449

F₁ (14)＝1000000000000001＝7×11×13×211×241×2161×9091

F₁ (15)＝10000000000000001＝353×449×641×1409×69857

F₁ (16)＝100000000000000001＝11×103×4013×21993833369

F₁ (17)＝1000000000000000001＝101×9901×999999000001

F₁ (18)＝10000000000000000001＝11×909090909090909091

F₁ (19)＝100000000000000000001＝73×137×1676321×5964848081

F₁ (20)＝1000000000000000000001＝7²×11×13×127×2689×459691×909091

F₁ (21)＝10000000000000000000001＝89×101×1052788969×1056689261

F₁ (22)＝100000000000000000000001＝11×47×139×2531×549797184491917

F₁ (23)＝1000000000000000000000001＝17×5882353×9999999900000001

F₁ (24)＝10000000000000000000000001＝11×251×5051×9091×78875943472201

F₁ (25)＝100000000000000000000000001＝101×521×1900381976777332243781

F₁ (26)＝1000000000000000000000000001＝7×11×13×19×52579×70541929×14175966169

F₁ (27)＝10000000000000000000000000001＝73×137×7841×127522001020150503761

F₁ (28)＝100000000000000000000000000001＝11×59×154083204930662557781201849

F₁ (29)＝1000000000000000000000000000001＝61×101×3541×9901×27961×4188901×39526741

F₁ (30)＝10000000000000000000000000000001＝11×909090909090909090909090909091

F₁ (31)＝100000000000000000000000000000001＝19841×976193×6187457×834427406578561

F₁ (32)＝1000000000000000000000000000000001＝7×11²×13×23×4093×8779×599144041×183411838171

记F₂(m)≡ ＝10101…01  (m个01)

F₂(1)＝101 ------质数

F₂(2)＝10101＝3×7×13×37

F₂(3)＝1010101＝73×101×137

F₂(4)＝101010101＝41×271×9091

F₂(5)＝10101010101＝3×7×13×37×101×9901

F₂(6)＝1010101010101＝239×4649×909091

F₂(7)＝101010101010101＝17×73×101×137×5882353

F₂(8)＝10101010101010101=3²×7×13×19×37×52579×333667

F₂(9)＝1010101010101010101＝41×101×271×3541×9091×27961

F₂(10)＝101010101010101010101＝11×23×4093×8779×21649×513239

F₂(11)＝10101010101010101010101＝3×7×13×37×73×101×137×9901×99990001

F₂(12)＝1010101010101010101010101＝29×101×239×281×4649×909091×121499449

F₂(13)＝101010101010101010101010101＝53×79×859×265371653×1058313049

F₂(14)＝10101010101010101010101010101＝3×7×13×31×37×41×211×241×271×2161×9091×2906161

F₂(15)＝1010101010101010101010101010101＝17×73×101×137×353×449×641×1409×69857×5882353

F₂(16)＝101010101010101010101010101010101＝103×4013×2071723×5363222357×21993833369

F₂(17)＝10101010101010101010101010101010101＝3²×7×13×19×37×101×9901×52579×333667×999999000001

F₂(18)＝1010101010101010101010101010101010101＝909090909090909091×1111111111111111111

记F₃(m)≡ ＝1001001…001  (m个001)F₃(1)＝1001＝7×11×13

F₃ (2)＝1001001＝3×333667

F₃ (3)＝1001001001＝7×11×13×101×9901

F₃ (4)＝1001001001001＝31×41×271×2906161

F₃ (5)＝1001001001001001＝3×7×11×13×19×52579×333667

F₃ (6)＝1001001001001001001＝43×239×1933×4649×10838689

F₃ (7)＝1001001001001001001001＝7×11×13×73×101×137×9901×99990001

F₃ (8)＝1001001001001001001001001＝3²×757×333667×440334654777631

F₃ (9)＝1001001001001001001001001001＝7×11×13×31×41×211×241×271×2161×9091×2906161

F₃ (10)＝1001001001001001001001001001001＝67×21649×513239×1344628210313298373

F₃ (11)＝1001001001001001001001001001001001＝3×7×11×13×19×101×9901×52579×333667×999999000001

F₃ (12)＝1001001001001001001001001001001001001＝53×79×265371653×900900900900990990990991

F₃ (13)＝1001001001001001001001001001001001001001＝7²×11×13×43×127×239×1933×2689×4649×459691×909091×10838689

F₃ (14)＝1001001001001001001001001001001001001001001＝3×31×41×271×238681×333667×2906161×4185502830133110721

F₃ (15)＝1001001001001001001001001001001001001001001001＝7×11×13×17×73×101×137×9901×5882353×99990001×9999999900000001

F₃ (16)＝1001001001001001001001001001001001001001001001001＝613×210631×2071723×52986961×5363222357×13168164561429877

F₃ (17)＝1001001001001001001001001001001001001001001001001001＝3²×7×11×13×19×757×52579×333667×70541929×14175966169×440334654777631

F₃ (18)＝1001001001001001001001001001001001001001001001001001001＝21319×10749631×1111111111111111111×3931123022305129377976519

记F₄(m)≡ ＝100010001…0001  (m个0001)

F₄(1)＝10001＝73×137

F₄(2)＝100010001＝3×7×13×37×9901

F₄(3)＝1000100010001＝17×73×137×5882353

F₄(4)＝10001000100010001＝41×271×3541×9091×27961

F₄(5)＝100010001000100010001＝3×7×13×37×73×137×9901×99990001

F₄(6)＝1000100010001000100010001＝29×239×281×4649×909091×121499449

F₄(7)＝10001000100010001000100010001＝17×73×137×353×449×641×1409×69857×5882353

F₄(8)＝100010001000100010001000100010001＝3²×7×13×19×37×9901×52579×333667×999999000001

F₄(9)＝1000100010001000100010001000100010001＝41×73×137×271×3541×9091×27961×1676321×5964848081

F₄(10)＝10001000100010001000100010001000100010001＝11×23×89×4093×8779×21649×513239×1052788969×1056689261

F₄(11)＝100010001000100010001000100010001000100010001＝3×7×13×17×37×73×137×9901×5882353×99990001×9999999900000001

记F₅(m)≡ ＝10000100001…00001  (m个00001)

F₅(1)＝100001＝11×9091

F₅(2)＝10000100001＝3×31×37×2906161

F₅(3)＝1000010000100001＝11×101×3541×9091×27961

F₅(4)＝100001000010000100001＝21401×25601×182521213001

F₅(5)＝10000100001000010000100001＝3×7×11×13×31×37×211×241×2161×9091×2906161

F₅(6)＝1000010000100001000010000100001＝71×239×4649×123551×102598800232111471

F₅(7)＝100001000010000100001000010000100001＝11×73×101×137×3541×9091×27961×1676321×5964848081

F₅(8)＝10000100001000010000100001000010000100001＝3²×31×37×238681×333667×2906161×4185502830133110721

F₅(9)＝1000010000100001000010000100001000010000100001＝11×251×5051×9091×21401×25601×182521213001×78875943472201

记F₆(m)≡ ＝1000001000001…000001  (m个000001)

F₆(1)＝1000001＝101×9901

F₆(2)＝1000001000001＝3×19×52579×333667

F₆(3)＝1000001000001000001＝73×101×137×9901×99990001

F₆(4)＝1000001000001000001000001＝31×41×211×241×271×2161×9091×2906161

F₆(5)＝1000001000001000001000001000001＝3×19×101×9901×52579×333667×999999000001

F₆(6)＝1000001000001000001000001000001000001＝7×43×127×239×1933×2689×4649×459691×909091×10838689

F₆(7)＝1000001000001000001000001000001000001000001＝17×73×101×137×9901×5882353×99990001×9999999900000001

记F₇(m)≡ ＝100000010000001…0000001  (m个0000001)

F₇(1)＝10000001＝11×909091

F₇(2)＝100000010000001＝3×37×43×1933×10838689

F₇(3)＝1000000100000010000001＝11×29×101×281×909091×121499449

F₇(4)＝10000001000000100000010000001＝41×71×271×123551×102598800232111471

F₇(5)＝100000010000001000000100000010000001＝3×7²×11×13×37×43×127×1933×2689×459691×909091×10838689

记F₈(m)≡ ＝10000000100000001…00000001  (m个00000001)

F₈(1)＝100000001＝17×5882353

F₈(2)＝10000000100000001＝3×7×13×37×9901×99990001

F₈(3)＝1000000010000000100000001＝17×353×449×641×1409×69857×5882353

F₈(4)＝100000001000000010000000100000001＝41×271×3541×9091×27961×1676321×5964848081

F₈(5)＝10000000100000001000000010000000100000001＝3×7×13×17×37×9901×5882353×99990001×9999999900000001

记F₉(m)≡ ＝1000000001000000001…000000001  (m个000000001)

F₉(1)＝1000000001＝7×11×13×19×52579

F₉(2)＝1000000001000000001＝3×757×440334654777631

F₉(3)＝1000000001000000001000000001＝7×11×13×19×101×9901×52579×999999000001

F₉(4)＝1000000001000000001000000001000000001＝31×41×271×238681×2906161×4185502830133110721

F₉(5)＝1000000001000000001000000001000000001000000001＝3×7×11×13×19×757×52579×70541929×14175966169×440334654777631

记F₁₀(m)≡ ＝100000000010000000001…0000000001  (m个0000000001)

F₁₀(1)＝10000000001＝101×3541×27961

F₁₀(2)＝100000000010000000001＝3×7×13×31×37×211×241×2161×2906161

F₁₀(3)＝1000000000100000000010000000001＝73×101×137×3541×27961×1676321×5964848081

F₁₀(4)＝10000000001000000000100000000010000000001＝251×5051×21401×25601×182521213001×78875943472201

记F₁₁(m)≡ ＝10000000000100000000001…00000000001  (m个00000000001)

F₁₁(1)＝100000000001＝11²×23×4093×8779

F₁₁(2)＝10000000000100000000001＝3×37×67×1344628210313298373

F₁₁(3)＝1000000000010000000000100000000001＝11²×23×89×101×4093×8779×1052788969×1056689261

F₁₁(4)＝100000000001000000000010000000000100000000001＝41×271×1321×62921×83251631×1300635692678058358830121

记F₁₂(m)≡ ＝1000000000001000000000001…000000000001  (m个000000000001)

F₁₂(1)＝1000000000001＝73×137×99990001

F₁₂(2)＝1000000000001000000000001＝3×19×52579×333667×999999000001

F₁₂(3)＝1000000000001000000000001000000000001＝17×73×137×5882353×99990001×9999999900000001

其他

110011＝11×73×137

1100110011＝3×7×11×13×37×9901

11001100110011＝11×17×73×137×5882353

110011001100110011＝11×41×271×3541×9091×27961

1100110011001100110011＝3×7×11×13×37×73×137×9901×99990001

11001100110011001100110011＝11×29×239×281×4649×909091×121499449

110011001100110011001100110011＝11×17×73×137×353×449×641×1409×69857×5882353

1100110011001100110011001100110011＝ 3²×7×11×13×19×37×9901×52579×333667×999999000001

11001100110011001100110011001100110011＝11×41×73×137×271×3541×9091×27961×1676321×5964848081

110011001100110011001100110011001100110011＝11²×23×89×4093×8779×21649×513239×1052788969×1056689261

1100110011001100110011001100110011001100110011＝

3×7×11×13×17×37×73×137×9901×5882353×99990001×9999999900000001

11001100110011001100110011001100110011001100110011＝

11×53×79×521×859×265371653×1058313049×1900381976777332243781

110011001100110011001100110011001100110011001100110011＝

11×29×73×137×239×281×4649×7841×909091×121499449×127522001020150503761

1100110011001100110011001100110011001100110011001100110011＝

           3×7×11×13×31×37×41×61×211×241×271×2161×3541

                       ×9091×9901×27961×2906161×4188901×39526741

11001100110011001100110011001100110011001100110011001100110011＝

           11×17×73×137×353×449×641×1409×19841×69857×976193

                         ×5882353×6187457×834427406578561

110011001100110011001100110011001100110011001100110011001100110011＝

11×103×4013×2071723×28559389×1491383821×5363222357×21993833369×2324557465671829

1100110011001100110011001100110011001100110011001100110011001100110011＝

       3²×7×11×13×19×37×73×137×3169×9901×52579×98641

                      ×333667×99990001×999999000001×3199044596370769

11001100110011001100110011001100110011001100110011001100110011001100110011＝

11×722817036322379041×909090909090909091×1111111111111111111×1369778187490592461

110011001100110011001100110011001100110011001100110011001100110011001100110011＝

     11×17×41×73×137×271×3541×9091×27961×1676321×5070721

                   ×5882353×5964848081××19721061166646717498359681

1100110011001100110011001100110011001100110011001100110011001100110011001100110011＝

     3×7²×11×13×29×37×43×127×239×281×1933×2689

                         ×4649×9901×226549×459691×

×909091×10838689×121499449×4458192223320340849

11001100110011001100110011001100110011001100110011001100110011001100110011001100110011＝11²×23×73×89×137×617×4093×8779×21649×513239×1052788969

       ×1056689261××16205834846012967584927082656402106953