Here are the latest result from the primary electins held Tuesday in 13 states: Arizona

Four-term Republican Sen. Barry Goldwater, 71 and suffering from a hip ailment, was unchallenged for renomination in the Gop primary. Bill Schulz, a millionaire businessman, defeated two other Democrats and is expected to run a spirited race against Goldwater this fall. Schulz, a former Republican and owner of many apartment buildings, dropped out of the 1978 Democratic primary for governor. He put nearly $1 million of his money into his senatorial campaign. Colorado

Howard (Bo) Callaway was narrowly edged out by Colorado Secretary of State Mary Estell Buchanan in a four way primary for the Republican nomination to oppose freshman Sen. Gary Hart. Hart, who was unopposed for the Democratic nonimation, has been tagged by the GOP as a prime target for defeat in November. Callaway, former Secretary of the Army, was forced to step down as former president Gerald Ford's campaign manager after he was accused of using his Pentagon position to gain favorable treatmen for his ski resort. Buchanan, a moderate, failed to win a position on the party ballot, and petitioned her way into the primary after weeks of court battles.

Buchanan's margin was so small that a mandatory runoff was possible Connecticut

Former New York senator James Buckley easily defeated state Senate Minority Leader Richard Buzzuto in the Republican primary.

Buckley will face Democratic noninee Rep. Christopher Dodd in the November election to fill the seat vacated by retiring senator Abraham Ribicoff. Buckley represented New York from 1971 to 1977. He was defeated by Daniel Parrick Moynihan.

Buckley, a nationally known conservative, ignored Buzzuto throughout the primary and outspent him by 5 to 1.

John Aristotle Phillips, who drew national attention for his dergraduate college thesis on how to design an atomic bomb, won the Democratic nomination for Congress from Fairfield County.

Philips heads a citizens' lobby promoting solar energy and just turned 25 in August. He will face five-term Rep. Stewart McKinney in November. 2 Florida

First-term Sen. Richard Stone finished on top but without a majority among six candidates for the Democratic nomination. He will compete Oct. 7 against second-place finisher Bill Gunter, the state insurance commissioner whom Stone beat in a 1974 runoff.

In a Republican field of six, Paula Hawkins, former chairman of the state's Public Service Commission outdistanced five other candidates. With absentee ballots remaining to be counted, Hawkins had slightly more than 50 percen of the vote, which would allow her to win the nomination outright.

In other races, Rep. Richard Kelly, facing trial next month in the Abscam scandal, was soundly trounced by two Republican challengers.

Freshman Rep. Edward Stack was defeated by attorney Alan Becker. Becker, a state representative, lost a runoff for the Democratic attorney general nomination in 1978. He has represented condominium residents in a district where the condominium population is important. Minnesota

All incumbent comgressmen either ran unopposed or won renomination handly. Nevada

Republican Sen. Paul Laxalt had the good fortune to be opposed in the primary by a candidate who didn't bother to campaign. Laxalt, who is Republican presidential nominee Ronald Reagan's national campaign chairman, will be challgned in November by former Democratic state senator Mary Gojack, who had no opposition for her party's nomination, and by Libertarian Party candidate Allen Hacker. New Hampshire Meldrim Thomson, the controversial former governor who once advocated arming the state's National Guard with nuclear weapons, coasted to an easy victory in the Republican primary for governor.

The conservative Thomson, seeking an unprecendented fourth term in the New Hampshiree statehouse, was defeated in 1978 by Democrat Hugh J. Gallen, who new is seeking reelection.

The GOP race for the Senate remained too close to call, with large blocks of votes still uncounted. Howevr, in a speech early yesterday, former state Attorney General Warren Rudman claimed victory in the 11-man race. The winner will run against Democratic Sen. John Durkin.

In the 1st Congressional District race among seven Republicans, former House Speaker Marshall Cobleigh led in the race to face incumbent Democrat Norman D'Amours, who had no primary challenge.

In the GOP contest for the 2nd Congressional District seat being vacated by James Cleveland, state Sen. Susan McLane conceded yesterday to Executive Councilor Judd Gregg. New york

In a major upset, Alfonse D'Amato defeated four-term Sen. Jacob Javits in the Republican primary. Javits, however, has announced he will run on the Liberal Party ticket, and the two men will face Rep. Elizabeth Holtzman, winner of the Democratic primary. Holtzman defeated former Miss America and New York consumer affairs adviser Bess Myerson, former New York mayor John Lindsay and John Santucci.

The finish precentages were D'Amato 56 and Javits 44; Hotlzman 41, Myerson 30, Lindsay 16 and Santucci 13.

Veteran New York congressman John Murph, indicted in the Abscam scandal, easily won renomination from Staten Island and lower Manahattan. Former lieutenant governor Mary Anne Krupsak won the Democratic nomination for Congress from the 30th District in upstate New York. Rhode Island

Democratic Gov. J. Joseph Garrahy and his Republican challenger, Vincent A. Cianci Jr., had no primary opposition. Two congressmen, Rep. Edeard Beard and Rep. Fernand St. Germain, comfortably beat back challenges to their renominations. Vermont

Stewart Ledbetter, who walked the length of the state to demonstrate frugality in contrast to his heavy spending opposition, won a six-way primary for the Republican nomination for the Senate. Ledbetter will face incumbent Patrick Lehy in November. Leahy is the only Democrat Vermont has ever sent to the Senate, and he is considered a prime GOP target in the coming election.

Ledbetter resigned as state banking and insurance commissioner earlier this year. His principal opponent, James Mullin, spent $700,000. Mullins, a self-proclaimed "clone of Ronald Reagan," waged the most expensive campaign in state history.

In the Democratic gubernatorial primary, Attorney General M. Jerome Diamond narrowly won the right to run against Republican Gov. Richard Snelling. Utah

Republican Sen. Jake Garn was unopposed for renomination and is heavily favored for reelection. Dan Berman, a Salt Lake City Attorney, emerged as the apparent winner of a close race against A. Stephen Dirks, mayor of Ogden, for Democratic nomination. Wisconsin

Former representative Robert W. Kasten Jr. won a four-way Republican primary and the opportunity to run against Democratic Sen. Gaylord Nelson in November. Nelson faced no primary oppostion.

Democratic Reps. Clement Zablocki and Henry Reuss, both from Milwaukee, won easily over token opposition. Wyoming

Republican Rep. Richard Cheney, White House chief of staff in the Ford administration, was unopposed for renomination. Jim Rogers won the Democratic primary for the state's only congressional seat, outdistancing three other candidates.