A prime which yields a different prime when turned upside down with reversals of both being two more different primes. more
The first 600 bemirps :
1061,
1091,
1601,
1901,
10061,
10091,
16001,
19001,
106861,
109891,
168601,
198901,
1106881,
1109881,
1606081,
1806061,
1809091,
1886011,
1889011,
1909081,
10806881,
10809881,
11061811,
11091811,
11609681,
11698691,
11816011,
11819011,
11906981,
11968961,
16061681,
16098661,
16166681,
16689061,
16880681,
16986911,
18608861,
18616061,
18616681,
18661681,
18666161,
18690611,
18860801,
18890801,
18908891,
18919091,
18919981,
18960911,
18991981,
18999191,
19068991,
19091981,
19199981,
19689611,
19880981,
19986091,
100688611,
100988911,
101060111,
101090111,
106061611,
106186681,
106198601,
106199801,
106888891,
106890011,
106891601,
106968691,
106996801,
108016891,
108019861,
108160081,
108190081,
108661901,
108661981,
108699601,
108966901,
108991601,
108991681,
109091911,
109166801,
109168901,
109189981,
109669801,
109698961,
109860011,
109861901,
109888861,
110068901,
110098601,
110600981,
110900681,
111060101,
111090101,
116088811,
116160601,
116686811,
116886001,
116898961,
116969891,
116999161,
118080161,
118080191,
118618891,
118686611,
118880611,
118880911,
118918861,
118989911,
119088811,
119190901,
119666191,
119696861,
119868691,
119889001,
119989811,
160008661,
160800881,
160980991,
161080811,
161188681,
161668961,
161899861,
161999611,
166086091,
166106981,
166168861,
166180081,
166800061,
166980881,
168668881,
168696911,
168819811,
168861661,
168888901,
168910801,
168998161,
169806181,
169866161,
169896901,
169898611,
180061801,
180081661,
180081991,
180091801,
181608961,
181908691,
186009011,
186199801,
186681601,
186881161,
186901991,
188008061,
188008091,
188086991,
188089661,
188866861,
188899891,
189006011,
189166801,
189601661,
189881191,
189981901,
190008991,
190680661,
190800881,
191080811,
191188981,
191666911,
191866891,
191998691,
196809181,
196868911,
196869601,
196899191,
198610801,
198668191,
198816811,
198888601,
198891991,
198969611,
198998881,
199089061,
199109681,
199180081,
199198891,
199680881,
199800091,
1006088861,
1006606801,
1006919981,
1006986881,
1006986991,
1008688981,
1008816181,
1008819181,
1008988681,
1009088891,
1009616681,
1009689661,
1009689881,
1009909801,
1010601181,
1010886661,
1010889991,
1010901181,
1016011991,
1016118011,
1016880191,
1016910161,
1019011661,
1019118011,
1019610191,
1019880161,
1060116901,
1060900081,
1061069861,
1061900911,
1061989601,
1069010011,
1069110901,
1069119991,
1069669661,
1069891601,
1069916891,
1069981111,
1080068911,
1080098611,
1080860861,
1080890891,
1081169681,
1081196981,
1086066001,
1086916091,
1088068181,
1088098181,
1088600911,
1088900611,
1089099001,
1089619061,
1090119601,
1090600081,
1091096891,
1091600611,
1091686901,
1096010011,
1096110601,
1096116661,
1096619861,
1096681111,
1096861901,
1096996991,
1100106901,
1100109601,
1101186161,
1101189191,
1106089891,
1108116101,
1108119101,
1109086861,
1110010661,
1110010991,
1110606181,
1110909181,
1111866901,
1111899601,
1116001961,
1116119891,
1118066681,
1118099981,
1119001691,
1119116861,
1160010191,
1160061901,
1160098801,
1160816161,
1160896081,
1160919691,
1161110191,
1161111661,
1161118891,
1166019611,
1166819081,
1166996191,
1168818661,
1168900801,
1168901681,
1169106611,
1169611061,
1169669191,
1180606991,
1180909661,
1181161691,
1181191961,
1190010161,
1190068801,
1190091601,
1190616961,
1190819191,
1190869081,
1191110161,
1191111991,
1191118861,
1196109911,
1196911091,
1196996161,
1198600801,
1198601981,
1198818991,
1199016911,
1199669161,
1199816081,
1601066161,
1601169611,
1601806961,
1606980961,
1608109991,
1609169801,
1610100911,
1610111911,
1610180161,
1610196101,
1610806991,
1610810161,
1610889101,
1611199861,
1611860981,
1616180611,
1616601061,
1616608691,
1616811011,
1616908861,
1616996911,
1619669911,
1660100111,
1661109101,
1661111611,
1666018091,
1666116901,
1666880101,
1668188611,
1669080191,
1669090811,
1669669081,
1669669601,
1669869001,
1680680801,
1680869081,
1681618181,
1681898081,
1686119111,
1686809011,
1688096161,
1688111911,
1688806001,
1688901691,
1688960881,
1689166901,
1689601601,
1689911161,
1690896061,
1691006111,
1691068891,
1691911811,
1696081061,
1696160911,
1698099191,
1698988981,
1699686181,
1800060901,
1800090601,
1806189911,
1806980611,
1806980891,
1806996991,
1808681891,
1808981861,
1809186611,
1809669661,
1809680861,
1809680911,
1811060101,
1811090101,
1816060111,
1816188001,
1816869961,
1818161861,
1818191891,
1818608801,
1818908801,
1819090111,
1819188001,
1819896691,
1860981191,
1861098611,
1866169001,
1866608111,
1868868691,
1868898001,
1869611801,
1880698861,
1880968891,
1886896001,
1889869001,
1890681161,
1891068911,
1896911801,
1898868001,
1898898961,
1899196001,
1899908111,
1901099191,
1901196911,
1901809691,
1906196801,
1908106661,
1909680691,
1910100611,
1910111611,
1910169101,
1910180191,
1910809661,
1910810191,
1910886101,
1911166891,
1911890681,
1916996611,
1919180911,
1919608891,
1919669611,
1919811011,
1919901091,
1919908961,
1960869091,
1961009111,
1961098861,
1961611811,
1966989181,
1968066161,
1968688681,
1969081091,
1969190611,
1980896081,
1980980801,
1981868081,
1981918181,
1986199601,
1986611191,
1986901901,
1988069191,
1988111611,
1988601961,
1988690881,
1988809001,
1989116111,
1989806011,
1990100111,
1991106101,
1991111911,
1996060811,
1996080161,
1996896001,
1996996081,
1996996901,
1998188911,
1999018061,
1999119601,
1999880101,
10000169111,
10000196111,
10006090181,
10008808661,
10008808991,
10009060181,
10011611111,
10011699011,
10011911111,
10011966011,
10016016091,
10019019061,
10060160881,
10060860181,
10060891691,
10061016991,
10061180891,
10061801681,
10066109891,
10068600901,
10068619661,
10068910091,
10068966881,
10069009091,
10069111681,
10069819091,
10069916861,
10080106691,
10080109961,
10086080861,
10086108601,
10086901991,
10089080891,
10089108901,
10089601661,
10090190881,
10090861961,
10090890181,
10091019661,
10091180861,
10091801981,
10096006061,
10096111981,
10096619891,
10096816061,
10098610061,
10098699881,
10098900601,
10098916991,
10099106861,
10100006011,
10100009011,
10100010601,
10100010901,
10100169601,
10100196901,
10100669611,
10100996911,
10101688111,
10101988111,
10106118881,
10106980861,
10109118881,
10109680891,
10110060601,
10110090901,
10110689111,
10110986111,
10116186811,
10116610661,
10118661811,
10118991811,
10119189811,
10119910991,
10160191091,
10160680681,
10161110801,
10161186881,
10161889181,
10166166611,
10166191081,
10166680691,
10168008881,
10168060081,
10169001691,
10169106881,
10169111801,
10169190991,
10169660161,
10169901901,
10180160911,
10180190611,
10186006891,
10188618161,
10188918191,
10189009861,
10190161061,
10190980981,
10191110801,
10191189881,
10191886181,
10196001961,
10196109881,
10196111801,
10196160661,
10196601601,
10196990191,
10198008881,
10198090081,
10199161081,
10199199911,
10199980961,
10600681811,
10600868081,
10600989001,
10601000101,
10601061011,
10601608081,
10601986691,
10601988181,
10606001101,
10606801811,
10608610891,
10608809891,
10609069901,
10609101961,
10609668911,
10610116961,
10610669101,
10611606961,
10611919811,
10616009011.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 237392 values, from 1061 to 199999990066801).
n\r | 0 | 1 |
2 | 0 | 237392 | 2 |
3 | 0 | 118988 | 118404 | 3 |
4 | 0 | 143097 | 0 | 94295 | 4 |
5 | 0 | 237392 | 0 | 0 | 0 | 5 |
6 | 0 | 118988 | 0 | 0 | 0 | 118404 | 6 |
7 | 0 | 39023 | 35643 | 41787 | 40346 | 40020 | 40573 | 7 |
8 | 0 | 76252 | 0 | 56535 | 0 | 66845 | 0 | 37760 | 8 |
9 | 0 | 39704 | 39100 | 0 | 39720 | 39344 | 0 | 39564 | 39960 | 9 |
10 | 0 | 237392 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 10 |
11 | 0 | 24632 | 23495 | 22198 | 25530 | 22731 | 23575 | 25276 | 21736 | 23833 | 24386 |
A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.