Block #316,963

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/17/2013, 9:29:35 AM · Difficulty 10.1495 · 6,475,681 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

14efcec3d29e41ddf6a183170ceddfc6279a5112039da83028b26678592cae79

View on Chainz ↗

Height

#316,963

Difficulty

10.149451

Transactions

Size

1.11 KB

Version

Bits

0a26426b

Nonce

206,735

Timestamp

12/17/2013, 9:29:35 AM

Confirmations

6,475,681

Merkle Root

b53dca2045181fd8499d9a89f546d7a37d43468637025e283e53c3d459381f8a

Transactions (1)

Coinbaseb53dca2045181f…53c3d459381f8a

1 in → 29 out9.6700 XPM1.02 KB

Ad9pSzHt…cpJ3y2zz Aac9Hjdg…P4ktypc3 Actx8HRL…1LEiodun AczNP7Qa…nfcLAodi AbtgNzNb…9Atvu81w

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.

6.596 × 10⁹⁶(97-digit number)

65967039645223478434…13457335889717373439

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

6.596 × 10⁹⁶(97-digit number)

65967039645223478434…13457335889717373439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.319 × 10⁹⁷(98-digit number)

13193407929044695686…26914671779434746879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.638 × 10⁹⁷(98-digit number)

26386815858089391373…53829343558869493759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.277 × 10⁹⁷(98-digit number)

52773631716178782747…07658687117738987519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.055 × 10⁹⁸(99-digit number)

10554726343235756549…15317374235477975039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.110 × 10⁹⁸(99-digit number)

21109452686471513098…30634748470955950079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.221 × 10⁹⁸(99-digit number)

42218905372943026197…61269496941911900159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.443 × 10⁹⁸(99-digit number)

84437810745886052395…22538993883823800319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.688 × 10⁹⁹(100-digit number)

16887562149177210479…45077987767647600639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.377 × 10⁹⁹(100-digit number)

33775124298354420958…90155975535295201279

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