Block #172,190

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/20/2013, 1:19:12 AM · Difficulty 9.8634 · 6,623,257 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

c852e22b6586304f5d31082c9f87dc424559ca98537a05bd7fc7e13b2e3b4a85

View on Chainz ↗

Height

#172,190

Difficulty

9.863414

Transactions

Size

947 B

Version

Bits

09dd08b7

Nonce

687,810

Timestamp

9/20/2013, 1:19:12 AM

Confirmations

6,623,257

Mined by

⛏️ P2SHAdKsRfZ9zYvTkJxCw18uWVLBrc8etcTibj

Merkle Root

fbd543c8736e37fba0b6e32f446c5e34726b424579c1a516e63d1b18bc8111da

Transactions (3)

Coinbase4726da5d00a462…f9b45155c89bd3

1 in → 1 out10.2800 XPM109 B

AdKsRfZ9…8etcTibj

5be4cacf50a258…9bb97530362861

3 in → 2 out5.0867 XPM522 B

AcuM7XiJ…5uND8Jce AVoCfiTP…iZWvxPv3

1cafdcc63c1bf3…29d147e652f155

1 in → 2 out2.8407 XPM225 B

AVkyZP2P…hpfN2udv AMmGeXac…8N1iWEtv

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.

3.404 × 10⁹⁷(98-digit number)

34044759001013532630…99972278140537288559

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

3.404 × 10⁹⁷(98-digit number)

34044759001013532630…99972278140537288559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.808 × 10⁹⁷(98-digit number)

68089518002027065261…99944556281074577119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.361 × 10⁹⁸(99-digit number)

13617903600405413052…99889112562149154239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.723 × 10⁹⁸(99-digit number)

27235807200810826104…99778225124298308479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.447 × 10⁹⁸(99-digit number)

54471614401621652208…99556450248596616959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.089 × 10⁹⁹(100-digit number)

10894322880324330441…99112900497193233919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.178 × 10⁹⁹(100-digit number)

21788645760648660883…98225800994386467839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.357 × 10⁹⁹(100-digit number)

43577291521297321767…96451601988772935679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.715 × 10⁹⁹(100-digit number)

87154583042594643534…92903203977545871359

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