Block #199,587

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/8/2013, 11:36:45 AM · Difficulty 9.8877 · 6,593,334 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

43a3ab8f67611d1d377672281d657c278cee5958ccf76a90a9055784e5f5423b

View on Chainz ↗

Height

#199,587

Difficulty

9.887716

Transactions

Size

4.56 KB

Version

Bits

09e34161

Nonce

1,164,878,163

Timestamp

10/8/2013, 11:36:45 AM

Confirmations

6,593,334

Merkle Root

1c56dcba67cd1a422b61a989d6b472ef63891b7f37db6be7aa8e48b465244852

Transactions (1)

Coinbase1c56dcba67cd1a…8e48b465244852

1 in → 133 out10.1600 XPM4.48 KB

AL6uGDJU…4gq3HbRu AWgwrQ5r…KVAzQwZ1 Ae54SB9E…Aow3zWsK AcNvVMY6…UfezsnjX AKtK4SH7…Ti8JpB2W

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.

2.608 × 10⁹³(94-digit number)

26086771287938032616…36084457707963567359

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

2.608 × 10⁹³(94-digit number)

26086771287938032616…36084457707963567359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.217 × 10⁹³(94-digit number)

52173542575876065232…72168915415927134719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.043 × 10⁹⁴(95-digit number)

10434708515175213046…44337830831854269439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.086 × 10⁹⁴(95-digit number)

20869417030350426092…88675661663708538879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.173 × 10⁹⁴(95-digit number)

41738834060700852185…77351323327417077759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.347 × 10⁹⁴(95-digit number)

83477668121401704371…54702646654834155519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.669 × 10⁹⁵(96-digit number)

16695533624280340874…09405293309668311039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.339 × 10⁹⁵(96-digit number)

33391067248560681748…18810586619336622079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.678 × 10⁹⁵(96-digit number)

66782134497121363497…37621173238673244159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.335 × 10⁹⁶(97-digit number)

13356426899424272699…75242346477346488319

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