Block #281,012

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/28/2013, 9:17:26 PM · Difficulty 9.9760 · 6,533,288 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bb5c44e0db92a8d00b4c8377026addcb4ff918a2bf92bb6a2d892906651cc15f

View on Chainz ↗

Height

#281,012

Difficulty

9.975998

Transactions

Size

1002 B

Version

Bits

09f9db05

Nonce

5,155

Timestamp

11/28/2013, 9:17:26 PM

Confirmations

6,533,288

Mined by

⛏️ IaRAZaXBzovMzme7PYvKWQ3unVWs3w3crVQYp

Merkle Root

a0ffabf08d11d6a9d2f091c414082bdb845d556c21d2e04536305e6f54be4ae2

Transactions (1)

Coinbasea0ffabf08d11d6…305e6f54be4ae2

1 in → 25 out10.0300 XPM913 B

AZaXBzov…w3crVQYp Ac7ndEyd…1EN9kFiR Ac6mGvmQ…XqWmPHjR AMbCuLHZ…WSoStwkc AcP9aGkN…9c7TeeiQ

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.

2.056 × 10⁹²(93-digit number)

20565328289653207144…48542673946331021919

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

2.056 × 10⁹²(93-digit number)

20565328289653207144…48542673946331021919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.113 × 10⁹²(93-digit number)

41130656579306414288…97085347892662043839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.226 × 10⁹²(93-digit number)

82261313158612828577…94170695785324087679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.645 × 10⁹³(94-digit number)

16452262631722565715…88341391570648175359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.290 × 10⁹³(94-digit number)

32904525263445131430…76682783141296350719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.580 × 10⁹³(94-digit number)

65809050526890262861…53365566282592701439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.316 × 10⁹⁴(95-digit number)

13161810105378052572…06731132565185402879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.632 × 10⁹⁴(95-digit number)

26323620210756105144…13462265130370805759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.264 × 10⁹⁴(95-digit number)

52647240421512210289…26924530260741611519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.052 × 10⁹⁵(96-digit number)

10529448084302442057…53849060521483223039

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

Block #281,012

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