Block #433,538

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/7/2014, 3:50:31 PM · Difficulty 10.3453 · 6,358,380 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

fc03862e632fc8ee2977d31e4f0c6e6960584bafc5f8411cc0e08b1efe6d7181

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Height

#433,538

Difficulty

10.345256

Transactions

Size

711 B

Version

Bits

0a5862ab

Nonce

57,378

Timestamp

3/7/2014, 3:50:31 PM

Confirmations

6,358,380

Merkle Root

653384cf6f9fe0f3521bee51f384e692a9ada7413a727965c18615a31c877ecf

Transactions (2)

Coinbase1d258faab5a7b3…de1e13e33d7119

1 in → 2 out9.3400 XPM131 B

AMVf7Jrg…xd5AVR7C AJno7LX2…vo4wdWtY

03093f558907cc…06c33200fc5d12

3 in → 1 out45.6926 XPM490 B

AH2DJpAP…wVCmD6dW

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.

5.087 × 10⁹⁴(95-digit number)

50870316704031266035…54621338827900296881

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

5.087 × 10⁹⁴(95-digit number)

50870316704031266035…54621338827900296881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.017 × 10⁹⁵(96-digit number)

10174063340806253207…09242677655800593761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.034 × 10⁹⁵(96-digit number)

20348126681612506414…18485355311601187521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.069 × 10⁹⁵(96-digit number)

40696253363225012828…36970710623202375041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.139 × 10⁹⁵(96-digit number)

81392506726450025656…73941421246404750081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.627 × 10⁹⁶(97-digit number)

16278501345290005131…47882842492809500161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.255 × 10⁹⁶(97-digit number)

32557002690580010262…95765684985619000321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.511 × 10⁹⁶(97-digit number)

65114005381160020524…91531369971238000641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.302 × 10⁹⁷(98-digit number)

13022801076232004104…83062739942476001281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.604 × 10⁹⁷(98-digit number)

26045602152464008209…66125479884952002561

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer