Block #508,553

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/24/2014, 11:17:25 AM · Difficulty 10.8189 · 6,296,537 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

517f51d2ac1be869671b85831676c98940575fa6268d83c8e90cd0523ff6fed2

View on Chainz ↗

Height

#508,553

Difficulty

10.818893

Transactions

Size

832 B

Version

Bits

0ad1a2f4

Nonce

199,026

Timestamp

4/24/2014, 11:17:25 AM

Confirmations

6,296,537

Mined by

⛏️ F=,AREQGaCCeRHuaNkf53p3iT4PbrV47D9Shh

Merkle Root

4be08a09ac09beb17fb82f80df626714d6f293bc23c29580529a70a9c2ad677c

Transactions (1)

Coinbase4be08a09ac09be…9a70a9c2ad677c

1 in → 20 out8.5300 XPM743 B

AREQGaCC…V47D9Shh AGz9gyZW…bo8NYQpw AMVf7Jrg…xd5AVR7C AUzEPJFG…kYkA5U9V AbHY4iza…Yckt2J5W

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.

2.233 × 10⁹²(93-digit number)

22337493227700290938…58127903606859875839

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

2.233 × 10⁹²(93-digit number)

22337493227700290938…58127903606859875839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.467 × 10⁹²(93-digit number)

44674986455400581877…16255807213719751679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.934 × 10⁹²(93-digit number)

89349972910801163754…32511614427439503359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.786 × 10⁹³(94-digit number)

17869994582160232750…65023228854879006719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.573 × 10⁹³(94-digit number)

35739989164320465501…30046457709758013439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.147 × 10⁹³(94-digit number)

71479978328640931003…60092915419516026879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.429 × 10⁹⁴(95-digit number)

14295995665728186200…20185830839032053759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.859 × 10⁹⁴(95-digit number)

28591991331456372401…40371661678064107519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.718 × 10⁹⁴(95-digit number)

57183982662912744802…80743323356128215039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.143 × 10⁹⁵(96-digit number)

11436796532582548960…61486646712256430079

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