What are the oldest nuclear wepons in the US arsenal?

I’m not asking about design; I’m wondering about the specific bombs or missiles or what have you.
Heck, for that matter: 'What’s the oldest physical nuclear weapon in the world?

For the US inventory, hile they’re no longer in operational service the Minuteman II motors of 1960s vintage are still being for sounding rocket and space launch applications in both operational and modified configurations. The only currently operational ICBM system is the LGM-30G 'Minuteman III", which underwent a remanufacturing program starting in thr late 1990s and ending in 2009. The current SLBM system is the UGM-133 ‘D-5 Trident II’, first deployed in 1990. The previous ‘C-4 Trident’ missiles are no longer in service but as with Minuteman II the motors are still used for other purposes, primarily as the propulsion system for targets used for anti-ballistic missile testing.

As for nuclear weapons, there is this table from nuclearweaponarchive.org, although it is ten years out of date. The W76 is still in service owing to a dearth of W88 warheads for Trident II and is undergoing a refurbishement/safety upgrade program. The W87–originally fielded on the now-retired LGM-118A 'Peacekeeper–has mostly replaced the W78 on the Minuteman III since they have gone away from the three MIRV configuration, and the B61-3/4 ‘Dial-A-Yield’ variable yield tactical gravity bombs are in the Inactive Stockpile but still available for use.

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Don’t forget they are being used for youtube video production!

I suspect that there’s a “grandfather’s axe” problem, here. Does it count if parts have been replaced? How many? What if it’s the core that’s replaced?

For missile system rebuilds such as the Minuteman Propulsion Replacement Program, the motors are essentially rebuilt; metallic cases have the propellant washed out and reused, fiber wound cases are discarded and built new; new propellent is poured to form the grain; mechanical and electrical components are refurbished or replaced. It is basically considered a new article and is issued a new top-level serial number.

For nuclear weapons, the refurbishment or upgrade is usually more subtle. Because we no longer have suitable production grade plutonium processing or uranium separation/enrichment facilities, the pits are generally reused as is. Any components damaged by neutron flux are replaced; krytron/sprytron devices are refurbished or replaced/upgraded; the chemical explosives are generally replaced; other enhancements may be added for safety and reliability. Many of the current B-61 pits are Mod 3/4 versions which were subsequently upgraded.

There are, however, unmodified original production articles of the MMII and C-4 missiles, and B-61 Mod 3/4 weapons from their respective vintages still in some form of use and long past their design service life.

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