は锣计

瓣计厩產皑紈 (Martin Gardner, 1914 - 2010)

癴计

癴计 (Reversible Prime) 嘿は计 (Emirp) 硂琌ぐ或㎡ウ璣ゅ会禣秆ㄥтぃ秆睦砛Τ琌瓣ゅиぃ礛

ㄓ Emirp 琌р璣ゅ Prime (计) は筁ㄓ (Reverse) ﹃τΘ璝计は筁ㄓ琌计硂獽琌癴计┪は计 硂秨ネ穝タ琌パ瓣计厩產皑紈 (Martin Gardner, 1914- 2010) ┮承籹

孔は筁ㄓ 13 => 31  149 => 941 单獽琌иノ计厩﹚竡ぃ糶ㄢㄒㄓ┪フ讽礛腨ㄓ弧琌ㄧ计砞计 p = an10n + an-110n-1 + ...... + a0 ㄤい ai  0 - 9 ぇ丁俱计

τ f(p) = a010n + a110n-1 + ...... + an

璝 f(p) 琌计p 獽琌は计ㄤ龟 f(p) 穦琌は计

礛10111 单癹ゅ计 (Palindromic Prime, Palprime) ゲ礛は锣は锣琌计ирウ埃は计﹚竡滦ぇ尔パは计ゲ礛琌蛮癸瞷 13 ㎝ 31  149 ㎝ 941 单

ê或иㄇ计琌は计㎡

13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, ... (OEIS A006567)

は计ぇ㎝

计籔は计ぇ㎝ (Sum of Prime and Emirp) Τ穦Τㄇ疭

ㄇ计㎝は计㎝琌琘计キよ 8362 = 303593 + 395303 = 333563 + 365333 = 342653 + 356243 = 344453 + 354443 = 348053 + 350843

 1232 =744377 + 773447 = 754367 + 763457 = 755267 + 762557硂ㄢ舱常琌パらセ筿福祘畍 Seiji Tomita т

ㄇ计㎝は计㎝琌タ琌癸计籔は计縩 (Product of Prime and Emirp) ㄢ1006441 + 1446001 = 2 * 1021 * 1201

硂琌パ风ㄥ癶ヰ祘Αㄈ狶 (Torbjorn Alm) т

硈尿瞷は计

硈尿癴计 (Consecutive Reversible Primes) ┪硈尿は计 (Consecutive Emirps) 琌硈尿瞷计は计 13, 17 は筁ㄓ 31 ㎝ 71 琌计硂獽癸 2 硈尿は计

糶ㄇぃ硈尿は计ㄒ

 程硈尿は计 は筁ㄓ计
2 13, 17 31, 71
3 71, 73, 79 17, 37, 97
4 1231, 1237, 1249, 1259 1321, 7321, 9421, 9521
5 1958711, 1958731, 1958753, 1958773, 1958777 1178591, 1378591, 3578591, 3778591, 7778591
6 18974551, 18974561, 18974581, 18974591, 18974623, 18974629 15547981, 16547981, 18547981, 19547981, 32647981, 92647981
7 9597192601, 9597192613, 9597192643, 9597192653, 9597192667, 9597192677, 9597192679 1062917959, 3162917959, 3462917959, 3562917959, 7662917959, 7762917959, 9762917959

癴计

瞶癴计 (Reversible Semiprime) 嘿は计 (Emirpimes) 硂琌は锣计琌计计璣ゅ Emirpimes 琌眖 Semiprime (计) いは筁ㄓ﹃τΘㄤい计琌计度パㄢ计τㄓ冈ǎぃ琌计琾计ゅ讽礛 は计ョぃ珹 121 单癹ゅ计 (Palindromic Semiprime) 珿硂は计琌蛮癸ǐи泊玡

は计ㄒ15, 26, 39, 49, 51, 58, 62, 85, 93, 94, 115, 122, 123, ... (OEIS A097393)

и╯は计だ眔

n
1
2
3
4
5
6
7
10n ずは计计ヘ
0
10
90
898
7200
60732
506724

徽Τぐ或稰谋иは计だ琌禫ㄓ禫祡波

 Emirp ㎝ Prime ┪ Emirpimes 琌眖 Semiprime ㄢ癸и稱癬硂砛琌璣ゅ单パダ舱Θゅ砰╰贺よ遏舱Θ迭粂いゅ砰╰い硂玱︽ぃ硄ぃ礛и计┪计痷ぃ穦琌ぐ或狥﹁

把σゅ膍の呼

Gardner, M. The Magic Numbers of Dr Matrix. Buffalo, New York : Prometheus, p. 230, 1985.

Rivera, C. "Problems & Puzzles: Puzzle 020 - Reversible Primes." http://www.primepuzzles.net/puzzles/puzz_020.htm.

Rivera, C. "Problems & Puzzles: Puzzle 506 - Reversible Primes Again." http://www.primepuzzles.net/puzzles/puzz_506.htm.

Rivera, C. "Problems & Puzzles: Puzzle 541 - Emirps Again." http://www.primepuzzles.net/puzzles/puzz_541.htm.

Weisstein, E. W. "Emirp." From MathWorld. http://mathworld.wolfram.com/Emirp.html.

Weisstein, E. W. "Emirpimes." From MathWorld. http://mathworld.wolfram.com/Emirpimes.html.