The word primogeniture is playable in Words With Friends™, no blanks required. Because it is longer than 7 letters, you would have to play off an existing word or do it in several moves.
Words With Friends™ Letter Score: 23
Highest Scoring Words With Friends™ Play In The Letters primogeniture
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Seven Letter Word Alert: (95 words)
egotrip, emoting, emperor, emptier, epitome, germier, gimpier, gourmet, goutier, grimier, grouper, groupie, grouter, grunter, gumtree, gunport, igniter, ignitor, impinge, imprint, impurer, inepter, inerter, integer, interim, meeting, mintier, minuter, miterer, mitogen, mounter, mountie, mourner, onetime, outgrin, peering, perming, permute, pigment, pimento, pioneer, pointer, porting, pouring, poutier, poutine, pouting, premier, prenote, preterm, priming, printer, protege, protein, prurigo, purring, regimen, regroup, regrout, reigner, reinput, reinter, remoter, remount, repiner, repoint, reprime, reprint, reprune, reroute, retimer, reunite, rioting, romping, rongeur, ropemen, routine, routing, rumping, runtier, runtime, teeming, tempore, termini, terpine, tiering, touring, treeing, trireme, trouper, umpteen, unmerge, unriper, uromere, uterine