The US military uses a designation system that was adopted in the interwar period that changed from an adoption year based system to an incremental one. What that meant was that instead of having weapons designated "U.S. Rifle, Caliber .30-06, Model 1903" or similarly, you'd have "U.S. Rifle, Caliber .30, M1." For every new rifle adopted, this would increment upwards.

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What leads to the apparent breaks in the system is that the designation system included a number of limited-adoption weapons under the rifle category. Going down the list, we have:

• Rifle, Caliber .30, M1 - M1 Garand
• Rifle, Caliber .22, M2 - a .22lr target rifle for training
• *nothing for M3 for unclear reasons*
• Rifle, Survival, Caliber .22 M4 - an aircrew survival rifle chambered in .22 Hornet
• Rifle, Subcaliber, Caliber .22 M5 - a subcaliber .22 trainer
• Rifle, Shotgun, Survival, Caliber .22/.410, M5 - an aircrew survival weapon with both a .410 and .22 Hornet barrel from H&R
• Rifle, Shotgun, Survival, Caliber .22/.410, M6 - similar to the M5, but made by Ithaca
• Rifle, Subcaliber, Caliber .30, M7 - a subcaliber training weapon chambered in 30-06
• Rifle, Spotting, Caliber .50, M8 - a .50 BMG spotting rifle for recoilless rifles
• Rifle, Subcaliber, Caliber .30, M9 - another subcaliber 30-06 training weapon
• *10 and 11 appear to be skipped as well*
• Rifle, Caliber .22, M12 - .22lr bolt-action trainer
• Rifle, Caliber .22, M13 - .22lr bolt-action trainer
• Rifle, 7.62mm, M14 - the M14 as designed and configured for use as a standard infantry rifle
• Rifle, 7.62mm, M15 - Squad Automatic version of the M14 intended to replace the M1918 Browning Automatic Rifle
• Rifle, 5.56mm, M16 - the M16 rifle

The system continues well beyond that. Notably, the system took on experimental designations later on, while earlier experimental and trials guns received the "T" desiggnation. For example, the M14 was known as the T47 during trials and the FN FAL was the T48. However, we'd see the Stoner 63 evaluated as the XM22 and XM23 (depending on the configuration) and the OICW program produce the XM29, despite none of those guns progressing to full adoption.

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There's a similar trend in other areas of equipment. The M1 carbine of WW2 fame was followed by the M2 carbine, which was just a select-fire standard for the M1 carbine that could be done without any permanent changes to the M1. The M3 carbine was an M2 carbine mounting an early infrared scope, with only ~3,000 produced. The M4 carbine breaks the trend and is an entirely different weapon - a carbine variant of the M16.