Block #318,517

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/18/2013, 11:05:55 AM · Difficulty 10.1606 · 6,480,513 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

fda42162b93b118900e83809a66fbd1538a5a960874d1e5a7bcd1fe81520feab

View on Chainz ↗

Height

#318,517

Difficulty

10.160553

Transactions

Size

1.04 KB

Version

Bits

0a291a07

Nonce

232,548

Timestamp

12/18/2013, 11:05:55 AM

Confirmations

6,480,513

Mined by

⛏️ 5aRtALHbRxMJUifv41AqfZNktB5BbbLEi9pifp

Merkle Root

3ac441d4ebcc0683d78d81eb5df455c63f5a97e5a2256aa1c0e832350bc0a40a

Transactions (1)

Coinbase3ac441d4ebcc06…e832350bc0a40a

1 in → 27 out9.6700 XPM981 B

ALHbRxMJ…LEi9pifp ASy3AE9X…ghJMwaMJ Aac9Hjdg…P4ktypc3 AcQf1KeZ…fhY2Cs14 AUsTcddg…Z78ayoFz

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.

6.050 × 10⁹¹(92-digit number)

60500704124606115389…76705960079144694559

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

6.050 × 10⁹¹(92-digit number)

60500704124606115389…76705960079144694559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.210 × 10⁹²(93-digit number)

12100140824921223077…53411920158289389119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.420 × 10⁹²(93-digit number)

24200281649842446155…06823840316578778239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.840 × 10⁹²(93-digit number)

48400563299684892311…13647680633157556479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.680 × 10⁹²(93-digit number)

96801126599369784623…27295361266315112959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.936 × 10⁹³(94-digit number)

19360225319873956924…54590722532630225919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.872 × 10⁹³(94-digit number)

38720450639747913849…09181445065260451839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.744 × 10⁹³(94-digit number)

77440901279495827698…18362890130520903679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.548 × 10⁹⁴(95-digit number)

15488180255899165539…36725780261041807359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.097 × 10⁹⁴(95-digit number)

30976360511798331079…73451560522083614719

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