Block #2,757,561

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.

6.519 × 10⁹⁶(97-digit number)

65195410275218110698…25694246771681218559

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

6.519 × 10⁹⁶(97-digit number)

65195410275218110698…25694246771681218559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.303 × 10⁹⁷(98-digit number)

13039082055043622139…51388493543362437119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.607 × 10⁹⁷(98-digit number)

26078164110087244279…02776987086724874239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.215 × 10⁹⁷(98-digit number)

52156328220174488559…05553974173449748479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.043 × 10⁹⁸(99-digit number)

10431265644034897711…11107948346899496959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.086 × 10⁹⁸(99-digit number)

20862531288069795423…22215896693798993919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.172 × 10⁹⁸(99-digit number)

41725062576139590847…44431793387597987839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.345 × 10⁹⁸(99-digit number)

83450125152279181694…88863586775195975679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.669 × 10⁹⁹(100-digit number)

16690025030455836338…77727173550391951359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.338 × 10⁹⁹(100-digit number)

33380050060911672677…55454347100783902719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

6.676 × 10⁹⁹(100-digit number)

66760100121823345355…10908694201567805439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^11 × origin − 1

1.335 × 10¹⁰⁰(101-digit number)

13352020024364669071…21817388403135610879

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 First 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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #2,757,561

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