[lrppbqqi] word primes

below are the 129 primes less than 27^2 = 729, written in big-endian base 27, using the following straightforward encoding of base-27 digits:

a=1 b=2 c=3 d=4 e=5 f=6 g=7 h=8 i=9 j=10 k=11 l=12 m=13 n=14 o=15 p=16 q=17 r=18 s=19 t=20 u=21 v=22 w=23 x=24 y=25 z=26

b c e g k m q s w ab ad aj an ap at az be bg bm bq bs by cb ch cp ct cv cz da de ds dw eb ed en ep ev fa fe fk fq fs gb gd gh gj gv hg hk hm hq hw hy ih in it iz ja jg jk jm jw kj kn kp kt lg lm lw ly mb mh mp mv na ne nk ns nw od on op oz pa pg pk pq py qb qd qh qt ra re rm rq rw sh sj ta tg tq tw ub ud uj ut uz ve vg vm vs vw vy wj wt wv wz xe xk xm xy yb yh yp yz zg zq zy

there are 9 1-digit primes and 120 2-digit primes.

the digits c f i l o r u x corresponding to multiples of 3 never occur as the last (units) digit, except for c by itself.

for 1- and 2-digit primes, we do not need a symbol to represent zero.  the first digit cannot be zero because that would be a useless leading zero.  if the second digit were zero, the number would be a multiple of 27, so not prime.

future work: consider a prime base so that all letters can occur in the units place.  deal with the special case "10" by ignoring it.  what two characters should we add to reach the 28 letters needed for base 29, and where in the alphabet should we add them?  or which 4 should we eliminate for base 23?  (probably wxyz.)

for the 2098 3-digit primes between 27^2 = 729 and 27^3 = 19683 below, we do need a symbol for zero as a middle character.  we choose dash (hyphen), mimicking English orthography.  (apostrophe was another good option.)

for 4-digit primes and larger (not explored), we could have multiple dashes in a row which are hard to distinguish in fonts that meld them into a single line, so some other symbol (e.g., apostrophe) for zero would be better.  or, do base 26 instead of base 27: there will be no words starting with a=0.  (or, make z the zeroth letter.  x is another good choice for zero, unlikely to begin a word.)

these primes could be the dictionary for a weird game of Scrabble.  blank is zero.  reorder the alphabet so that the frequency of Scrabble letter tiles correspond to the frequency of letters among 2-digit primes.

which English words are primes?  this should be easy.  assuming we stick with base 27, choose a different mapping of letters to digits so that multiples of 3 correspond to the letters least likely to end a word.  or begin a word if encoding little-endian.  find the mapping of letters to digits that maximizes the number of prime English words.

a-d a-j a-n a-v aaa aae aam aaq abd abn abz aca ack acm acq acs adb adp adt adv adz aem aeq aes aew afp aft aga agk ags agw ahb ahh ahv ahz aie aik ais aiy ajj ajn ajt ajv ake akg akm akw aky alh alj alp amg amk amm amq amw anb anj anp anv aoq aos apb apj apt apz aqe aqm aqy arb arh arn arp arv asg asq ath atj atn att atv aua aue aug auk auw auy avd awk awq aww axd axv aye ays ayw ayy azb azh azp azt azv b-a b-m b-w b-y bab bad bah ban baz bbk bbs bcd bcj bcn bct bda bde bdm bdq bed beh ben bep bet bez bfa bfg bfq bgj bgp bgt bgv bhs bhw bhy bih bit biv bje bjm bjs bjy bkd bkv bla ble blg bls bmb bmn bmv bnk bny bod boh boj bon bop boz bpk bpq bpw bqn bqp bre brg bsb bsh bsp bsv bsz bta bte btm bts bub bud bun bva bvk bvq bwb bwd bwh bwj bwt bxe bxg bxw bxy byd byh byj byt bza bzs c-p c-t c-z cag caw cay cbb cbj cbz cca cce ccm ccs ccy cdb cdn cdp cek ceq ces cey cfb cfh cfv cga cge cgg cgm cgq cgw chh chn cht cig cik ciq cjb cjj cjp cjt cks clj clt cma cme cmk cmm cms cnn cnz coa coq coy cpb cpn cqa cqk cqm cqq cqy crd crj crn crp crt crz csg csk csm css ctb ctd ctn ctv ctz cum cuw cvh cvj cvp cvt cvv cwk cwy cxb cxh cxp cxv cxz cyq cyy czh czn czt d-a d-k d-w daj dan dat daz dba dcb dcd dcn dcv dcz ddm ddq ddy dej dep dfa dfe dfk dgd dgn dgp dhe did dih dij div dja dje djq djw dkd dkh dkp dlk dlm dlq dls dmd dne dng dnm dns dny dob doh doj dov doz dpk dpm dpw dpy dqn dqp dre drk dsd dst dta dte dtg dtk dtm duh dup dva dvg dvq dvs dvw dwb dwd dwj dwt dwv dxg dxq dxs dyb dyp dyv dyz dze dzm dzs dzy e-n e-z eaa eae eas eay ebb ebj ebt eca ecg ecm edh edn edp edz eem eeq eew efn efp efz egm egq egs ehb ehp eht eia eis eiw ejb ejd ejh ejn ejp eka eke eky elt eme emg emk emq emw emy end enz eoa eog eow epb epn epp epv eqg eqw eqy erb erh erv erz esa ess etp etz eue eug euq eus evb evd evn evt evv ewe ewg ewq eww exd eyg eyq eys ezb ezj ezp ezz f-q f-w fah fat fav fbm fbs fbw fcb fch fcz fda fdk fdy fed feh fej fen ffk ffm ffy fgd fgt fha fhg fhm fid fit fiv fiz fje fjg 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