Washington ? Shortly after nuclear weapons sleuths Tom Cochran and Bill Arkin published their unauthorized estimate of the size of the U.S. arsenal in 1984, they got a call from alarmed U.S. officials.

“They called us over and wanted to know where we got the numbers,” Cochran recalls from a time when almost everything about history’s deadliest weapon — including how many the U.S. possessed — was classified secret. It was a culture of secrecy born during the Cold War, out of a belief that nuclear candor could be dangerous.

America’s official nuclear silence ended Monday when the Obama administration not only disclosed the number of U.S. nuclear weapons available for use in wartime — 5,113 as of last Sept. 30 — but surprised many by also publishing weapons totals for each year dating to 1962. (Pre-1962 data was released in 1993.)

Secretary of State Hillary Rodham Clinton said the disclosures prove the U.S. is doing its part for disarmament.

The move also puts pressure on Russia, the world’s other main nuclear power, to provide similar accounting as the two sides consider following up their new START arms reduction treaty with a more comprehensive accord.

The U.S. disclosure didn’t just strike a blow for transparency in the global debate over nuclear weapons. It revealed the remarkable accuracy of the effort by Cochran, Arkin and others, who labored for 30 years to pull back the veil that surrounded these weapons.

“We were pretty close all along — sometimes right on the button,” said Robert S. Norris, another of the nuclear number detectives.

Their most recent estimate was 5,100, or just 13 weapons fewer than the number the government published Monday.

The total reflects the combined total of the nuclear-tipped missiles and bombs that U.S. forces have available for wartime use. It does not include an estimated 4,500 retired warheads that are in storage awaiting dismantlement.

Many official nuclear secrets remain, although they arguably are secret in name only. It’s widely known, for example — but not officially confirmed — that building a bomb takes almost 4 kilograms, or more than 8 pounds, of plutonium.

The administration has made no public commitment to publishing updated stockpile numbers in the future, but Cochran believes the logic of disclosing the current number implies that it will be updated annually.

Norris, author of a biography of Leslie R. Groves, the Army general who led the Manhattan Project that built the world’s first atomic bomb in 1945, said the cocoon of secrecy that enveloped the U.S. nuclear program grew out of a belief that the very survival of the nation was at stake.

“It was always, ‘The Russians are coming. Don’t bother us'” about openness, Norris said.

In the foreword to the government’s official account of the bomb project, published after the August 1945 attacks on Hiroshima and Nagasaki, Groves offered a word of warning for anyone, inside the government or out, who might feel a need to ask for details beyond those in the official book.

“Persons disclosing or securing additional information by any means whatsoever without authorization are subject to severe penalties under the Espionage Act,” Groves wrote.

Secrecy aside, Cochran and Arkin produced in 1984 the first volume of their encyclopedic “Nuclear Weapons Databook,” compiled from mining a mountain of responses to Freedom of Information Act requests and from years of scouring congressional hearing transcripts, unclassified government reports, budgets and other open records.

It was, in the view of McGeorge Bundy, who served as national security adviser to President John F. Kennedy, a historic victory for “private clarification” over “government obfuscation.” Bundy praised the 340-page work in a New York Times Book Review article in March 1984.

“This volume,” he wrote, “contains more facts about the past, present and future of such forces than have ever been put in one place before.”

No doubt that is why Cochran and Arkin got the phone call from the Energy Department once their book hit the stores.

“They couldn’t believe we had the numbers. They thought there was a leak in the system,” Cochran said. He and Norris work for the Natural Resources Defense Council, an environmental group.

In 1984, the nuclear detectives estimated that the U.S. that year had 26,000 weapons — although they subsequently refined the figure for 1984 to 23,717.

On Monday, they learned the actual total was 23,459, just 258 warheads off the mark.