Block #132,917

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/25/2013, 5:38:14 AM · Difficulty 9.7905 · 6,657,011 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

8ad1ade48a26570715f0d7d1d5a240de16e0bf8817745bd567fc6824ab5fe684

View on Chainz ↗

Height

#132,917

Difficulty

9.790515

Transactions

Size

198 B

Version

Bits

09ca5f30

Nonce

175,271

Timestamp

8/25/2013, 5:38:14 AM

Confirmations

6,657,011

Merkle Root

84d8dfb8a1f5f2f20da3206f400c2a1fe0218168623ffc5659c9a6bd13683769

Transactions (1)

Coinbase84d8dfb8a1f5f2…c9a6bd13683769

1 in → 1 out10.4200 XPM109 B

ARC4vboi…MTWaUQtV

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.

2.931 × 10⁹³(94-digit number)

29319480328139697326…89295391802374992239

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

2.931 × 10⁹³(94-digit number)

29319480328139697326…89295391802374992239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.863 × 10⁹³(94-digit number)

58638960656279394653…78590783604749984479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.172 × 10⁹⁴(95-digit number)

11727792131255878930…57181567209499968959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.345 × 10⁹⁴(95-digit number)

23455584262511757861…14363134418999937919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.691 × 10⁹⁴(95-digit number)

46911168525023515722…28726268837999875839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.382 × 10⁹⁴(95-digit number)

93822337050047031445…57452537675999751679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.876 × 10⁹⁵(96-digit number)

18764467410009406289…14905075351999503359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.752 × 10⁹⁵(96-digit number)

37528934820018812578…29810150703999006719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.505 × 10⁹⁵(96-digit number)

75057869640037625156…59620301407998013439

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer