Block #284,050

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/29/2013, 11:51:11 PM · Difficulty 9.9821 · 6,511,278 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bd2de20f67a3845ef6fc41db7c42e4101c1e47875ccad011d3da0fba9dddf331

View on Chainz ↗

Height

#284,050

Difficulty

9.982056

Transactions

Size

1.11 KB

Version

Bits

09fb6803

Nonce

41,819

Timestamp

11/29/2013, 11:51:11 PM

Confirmations

6,511,278

Mined by

⛏️ UaRAahbzMCBNWKFYkiMoRc7vE9Y1imFJF5Kys

Merkle Root

3f33a996dcdbe5d72af87727d091fb55bbf7b599f349e9f09ced3be812403228

Transactions (1)

Coinbase3f33a996dcdbe5…ed3be812403228

1 in → 29 out10.0000 XPM1.02 KB

AahbzMCB…mFJF5Kys AYRNBPg5…3q2SvNy5 AaN3X4nJ…7DX2KLvh APGjycSM…dcqEaFfQ AKde1i4d…88R1bw6g

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.

8.504 × 10⁹⁶(97-digit number)

85040501786900940677…04935002977922871779

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

8.504 × 10⁹⁶(97-digit number)

85040501786900940677…04935002977922871779

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.700 × 10⁹⁷(98-digit number)

17008100357380188135…09870005955845743559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.401 × 10⁹⁷(98-digit number)

34016200714760376270…19740011911691487119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.803 × 10⁹⁷(98-digit number)

68032401429520752541…39480023823382974239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.360 × 10⁹⁸(99-digit number)

13606480285904150508…78960047646765948479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.721 × 10⁹⁸(99-digit number)

27212960571808301016…57920095293531896959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.442 × 10⁹⁸(99-digit number)

54425921143616602033…15840190587063793919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.088 × 10⁹⁹(100-digit number)

10885184228723320406…31680381174127587839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.177 × 10⁹⁹(100-digit number)

21770368457446640813…63360762348255175679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.354 × 10⁹⁹(100-digit number)

43540736914893281626…26721524696510351359

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