Block #289,214

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 12/2/2013, 2:38:02 AM · Difficulty 9.9883 · 6,514,673 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

bec50d3f00d13317690d2578455e004f27fa781c08263c07d51bde78c3c075eb

View on Chainz ↗

Height

#289,214

Difficulty

9.988349

Transactions

Size

1.11 KB

Version

Bits

09fd0479

Nonce

9,845

Timestamp

12/2/2013, 2:38:02 AM

Confirmations

6,514,673

Mined by

⛏️ iaRAWrpzrQNLaaK3imQVGBSdGPBoGAxvr5NSY

Merkle Root

97a941f551dbe3223b7c15603cb974f51f6f1092dd9376d0f511d963a5022862

Transactions (1)

Coinbase97a941f551dbe3…11d963a5022862

1 in → 29 out9.9900 XPM1.02 KB

AWrpzrQN…Axvr5NSY AKEwr54i…9BfmMkRh AHAi4PDp…e5tL4csy AYcLTeXR…bscgPops AGXewNDY…FgKQN3gK

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.

2.178 × 10⁹¹(92-digit number)

21782881922023979045…49699116876291811321

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

2.178 × 10⁹¹(92-digit number)

21782881922023979045…49699116876291811321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.356 × 10⁹¹(92-digit number)

43565763844047958090…99398233752583622641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.713 × 10⁹¹(92-digit number)

87131527688095916180…98796467505167245281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.742 × 10⁹²(93-digit number)

17426305537619183236…97592935010334490561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.485 × 10⁹²(93-digit number)

34852611075238366472…95185870020668981121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.970 × 10⁹²(93-digit number)

69705222150476732944…90371740041337962241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.394 × 10⁹³(94-digit number)

13941044430095346588…80743480082675924481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.788 × 10⁹³(94-digit number)

27882088860190693177…61486960165351848961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.576 × 10⁹³(94-digit number)

55764177720381386355…22973920330703697921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.115 × 10⁹⁴(95-digit number)

11152835544076277271…45947840661407395841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.230 × 10⁹⁴(95-digit number)

22305671088152554542…91895681322814791681

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer