Block #251,424

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/9/2013, 12:44:33 AM · Difficulty 9.9698 · 6,581,098 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

77e6e6578a4bef966d146615e9de83b005cccd987426cfb3047a3e396b94347b

View on Chainz ↗

Height

#251,424

Difficulty

9.969820

Transactions

Size

2.08 KB

Version

Bits

09f84624

Nonce

150,209

Timestamp

11/9/2013, 12:44:33 AM

Confirmations

6,581,098

Mined by

⛏️ aR}GnAHEgP7WVNYzYHYg8UMCtqsqiFZ9jVoCDtB

Merkle Root

ed7324832eb9613e5c9b85d997264b6af04f688c41d658d8328b74d76c87224b

Transactions (1)

Coinbaseed7324832eb961…8b74d76c87224b

1 in → 58 out10.0200 XPM1.99 KB

AHEgP7WV…9jVoCDtB AdnG9gQ7…N9B7mA2p AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY ANo4YY1x…vnsPRDSU

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.

3.051 × 10⁹³(94-digit number)

30510850128166235069…48029024246918348799

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

3.051 × 10⁹³(94-digit number)

30510850128166235069…48029024246918348799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.102 × 10⁹³(94-digit number)

61021700256332470138…96058048493836697599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.220 × 10⁹⁴(95-digit number)

12204340051266494027…92116096987673395199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.440 × 10⁹⁴(95-digit number)

24408680102532988055…84232193975346790399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.881 × 10⁹⁴(95-digit number)

48817360205065976111…68464387950693580799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.763 × 10⁹⁴(95-digit number)

97634720410131952222…36928775901387161599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.952 × 10⁹⁵(96-digit number)

19526944082026390444…73857551802774323199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.905 × 10⁹⁵(96-digit number)

39053888164052780888…47715103605548646399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.810 × 10⁹⁵(96-digit number)

78107776328105561777…95430207211097292799

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

Block #251,424

Cookie Preferences