Block #191,612

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/3/2013, 6:52:15 AM · Difficulty 9.8752 · 6,600,856 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b6e063ea4829e00f33bf2c1ef0c5cae54ff79392e7e2499afe13f26fe1054fea

View on Chainz ↗

Height

#191,612

Difficulty

9.875204

Transactions

Size

205 B

Version

Bits

09e00d63

Nonce

33,558,139

Timestamp

10/3/2013, 6:52:15 AM

Confirmations

6,600,856

Merkle Root

3299756649ef3102c35b1d4e76071bd74233200cfe4f8570b8d574c19f1ea706

Transactions (1)

Coinbase3299756649ef31…d574c19f1ea706

1 in → 1 out10.2400 XPM116 B

AcLBm5Z9…S683d7c3

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.

1.930 × 10⁹²(93-digit number)

19308984715336108365…36061189513478921279

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

1.930 × 10⁹²(93-digit number)

19308984715336108365…36061189513478921279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.861 × 10⁹²(93-digit number)

38617969430672216730…72122379026957842559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.723 × 10⁹²(93-digit number)

77235938861344433460…44244758053915685119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.544 × 10⁹³(94-digit number)

15447187772268886692…88489516107831370239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.089 × 10⁹³(94-digit number)

30894375544537773384…76979032215662740479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.178 × 10⁹³(94-digit number)

61788751089075546768…53958064431325480959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.235 × 10⁹⁴(95-digit number)

12357750217815109353…07916128862650961919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.471 × 10⁹⁴(95-digit number)

24715500435630218707…15832257725301923839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.943 × 10⁹⁴(95-digit number)

49431000871260437414…31664515450603847679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.886 × 10⁹⁴(95-digit number)

98862001742520874829…63329030901207695359

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