Block #289,914

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/2/2013, 10:39:03 AM · Difficulty 9.9889 · 6,516,250 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

4a28bd2981d621a8f6caf3ba72e3fadb0167410c29980dda548e75cb43db9c74

View on Chainz ↗

Height

#289,914

Difficulty

9.988868

Transactions

Size

1.01 KB

Version

Bits

09fd2676

Nonce

221,609

Timestamp

12/2/2013, 10:39:03 AM

Confirmations

6,516,250

Mined by

⛏️ zlaRcAXydriH2y7rX2Yn566tsziBzZxRUoBRJjB

Merkle Root

c4e8ac3cb060506e5677d22dd49401ca57d34b3e08fe19b0284941d64b1e4391

Transactions (1)

Coinbasec4e8ac3cb06050…4941d64b1e4391

1 in → 26 out10.0100 XPM947 B

AXydriH2…RUoBRJjB AQAX2v64…6CKTrG2b AJzWx2VD…j4ZSMit5 AHuJ9wYh…BGmgHrKZ AXLJzdRc…LJLLZDBD

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.

7.865 × 10⁹²(93-digit number)

78657727189736679301…40456896912888212479

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

7.865 × 10⁹²(93-digit number)

78657727189736679301…40456896912888212479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.573 × 10⁹³(94-digit number)

15731545437947335860…80913793825776424959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.146 × 10⁹³(94-digit number)

31463090875894671720…61827587651552849919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.292 × 10⁹³(94-digit number)

62926181751789343441…23655175303105699839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.258 × 10⁹⁴(95-digit number)

12585236350357868688…47310350606211399679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.517 × 10⁹⁴(95-digit number)

25170472700715737376…94620701212422799359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.034 × 10⁹⁴(95-digit number)

50340945401431474753…89241402424845598719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.006 × 10⁹⁵(96-digit number)

10068189080286294950…78482804849691197439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.013 × 10⁹⁵(96-digit number)

20136378160572589901…56965609699382394879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.027 × 10⁹⁵(96-digit number)

40272756321145179802…13931219398764789759

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