Block #167,311

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/16/2013, 12:42:47 PM · Difficulty 9.8685 · 6,623,774 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b29863c846d3de1f1cd11e61705102e4473c02f5dd19b2df7a346814507944e1

View on Chainz ↗

Height

#167,311

Difficulty

9.868478

Transactions

Size

8.43 KB

Version

Bits

09de5491

Nonce

366,336

Timestamp

9/16/2013, 12:42:47 PM

Confirmations

6,623,774

Merkle Root

7a3e18b7f346474351e688542e84eeafdc4440a81bbbe4b9b9aaa869dddb221e

Transactions (2)

Coinbase6b4543ff7563a1…63d8323b39b554

1 in → 1 out10.3400 XPM109 B

AHTCuref…ciGEetrY

455be68384e4d4…3657972a4f34f1

73 in → 2 out740.1800 XPM8.24 KB

ATgTXu3k…iLAydbkp ALJo9bq8…zf32uzbF

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.

1.893 × 10⁹³(94-digit number)

18937882681261653297…51081898889402224001

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

1.893 × 10⁹³(94-digit number)

18937882681261653297…51081898889402224001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.787 × 10⁹³(94-digit number)

37875765362523306595…02163797778804448001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.575 × 10⁹³(94-digit number)

75751530725046613190…04327595557608896001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.515 × 10⁹⁴(95-digit number)

15150306145009322638…08655191115217792001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.030 × 10⁹⁴(95-digit number)

30300612290018645276…17310382230435584001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.060 × 10⁹⁴(95-digit number)

60601224580037290552…34620764460871168001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.212 × 10⁹⁵(96-digit number)

12120244916007458110…69241528921742336001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.424 × 10⁹⁵(96-digit number)

24240489832014916221…38483057843484672001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.848 × 10⁹⁵(96-digit number)

48480979664029832442…76966115686969344001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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