Block #314,724

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/16/2013, 3:09:46 AM · Difficulty 10.0718 · 6,490,482 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a608b57735aa17f0546f749dc5df34e115b000cfd656d6cdf976b1d9a3b86bef

View on Chainz ↗

Height

#314,724

Difficulty

10.071796

Transactions

Size

1004 B

Version

Bits

0a126133

Nonce

503,544

Timestamp

12/16/2013, 3:09:46 AM

Confirmations

6,490,482

Mined by

⛏️ daRpAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

fd2e924102539df158a44e5417cb5050a775f225ce4143933c3e86dcc6538861

Transactions (1)

Coinbasefd2e924102539d…3e86dcc6538861

1 in → 25 out9.8400 XPM913 B

Ad9pSzHt…cpJ3y2zz AbtgNzNb…9Atvu81w Aac9Hjdg…P4ktypc3 Acskt6D1…Db4ci1L8 AZuKpVkB…HFoeLG6t

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.

7.235 × 10⁹⁷(98-digit number)

72353969817929391900…45417485638078054399

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

7.235 × 10⁹⁷(98-digit number)

72353969817929391900…45417485638078054399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.447 × 10⁹⁸(99-digit number)

14470793963585878380…90834971276156108799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.894 × 10⁹⁸(99-digit number)

28941587927171756760…81669942552312217599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.788 × 10⁹⁸(99-digit number)

57883175854343513520…63339885104624435199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.157 × 10⁹⁹(100-digit number)

11576635170868702704…26679770209248870399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.315 × 10⁹⁹(100-digit number)

23153270341737405408…53359540418497740799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.630 × 10⁹⁹(100-digit number)

46306540683474810816…06719080836995481599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.261 × 10⁹⁹(100-digit number)

92613081366949621633…13438161673990963199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.852 × 10¹⁰⁰(101-digit number)

18522616273389924326…26876323347981926399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.704 × 10¹⁰⁰(101-digit number)

37045232546779848653…53752646695963852799

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