Block #424,588

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/1/2014, 8:13:11 AM · Difficulty 10.3588 · 6,389,711 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

420ee0973093c9c9099335a9cd1d5c4a807c467d6f0f16ad4daed901037ca4f4

View on Chainz ↗

Height

#424,588

Difficulty

10.358759

Transactions

Size

834 B

Version

Bits

0a5bd79b

Nonce

128,807

Timestamp

3/1/2014, 8:13:11 AM

Confirmations

6,389,711

Mined by

⛏️ zaS6AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c2c29dcb56f2fca66d904af70132bee43fc5e979a0c0cc89ffe77f58fc65a3b5

Transactions (1)

Coinbasec2c29dcb56f2fc…e77f58fc65a3b5

1 in → 20 out9.3100 XPM743 B

AQvZBsUo…hppgRZTJ AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

Prime Chain Origin

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.

5.458 × 10⁹⁶(97-digit number)

54589206464696094091…09428634737324102399

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

5.458 × 10⁹⁶(97-digit number)

54589206464696094091…09428634737324102399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.091 × 10⁹⁷(98-digit number)

10917841292939218818…18857269474648204799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.183 × 10⁹⁷(98-digit number)

21835682585878437636…37714538949296409599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.367 × 10⁹⁷(98-digit number)

43671365171756875273…75429077898592819199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.734 × 10⁹⁷(98-digit number)

87342730343513750546…50858155797185638399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.746 × 10⁹⁸(99-digit number)

17468546068702750109…01716311594371276799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.493 × 10⁹⁸(99-digit number)

34937092137405500218…03432623188742553599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.987 × 10⁹⁸(99-digit number)

69874184274811000437…06865246377485107199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.397 × 10⁹⁹(100-digit number)

13974836854962200087…13730492754970214399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.794 × 10⁹⁹(100-digit number)

27949673709924400174…27460985509940428799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #424,588

Cookie Preferences