Block #2,924,966

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.590 × 10⁹⁶(97-digit number)

25902526386830262736…00999025637255307521

Discovered Prime Numbers

p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin + 1

2.590 × 10⁹⁶(97-digit number)

25902526386830262736…00999025637255307521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.180 × 10⁹⁶(97-digit number)

51805052773660525473…01998051274510615041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.036 × 10⁹⁷(98-digit number)

10361010554732105094…03996102549021230081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.072 × 10⁹⁷(98-digit number)

20722021109464210189…07992205098042460161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.144 × 10⁹⁷(98-digit number)

41444042218928420378…15984410196084920321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.288 × 10⁹⁷(98-digit number)

82888084437856840757…31968820392169840641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.657 × 10⁹⁸(99-digit number)

16577616887571368151…63937640784339681281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.315 × 10⁹⁸(99-digit number)

33155233775142736303…27875281568679362561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.631 × 10⁹⁸(99-digit number)

66310467550285472606…55750563137358725121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.326 × 10⁹⁹(100-digit number)

13262093510057094521…11501126274717450241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.652 × 10⁹⁹(100-digit number)

26524187020114189042…23002252549434900481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

5.304 × 10⁹⁹(100-digit number)

53048374040228378085…46004505098869800961

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★★☆

Rarity

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #2,924,966

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