Block #245,103

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/5/2013, 6:51:42 AM · Difficulty 9.9635 · 6,562,801 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bf9c06daed5ebc888aec180659d5c1831c7687de6227a6c3fe2f20ae8c5d9101

View on Chainz ↗

Height

#245,103

Difficulty

9.963451

Transactions

Size

198 B

Version

Bits

09f6a4ba

Nonce

301,277

Timestamp

11/5/2013, 6:51:42 AM

Confirmations

6,562,801

Mined by

⛏️ P2SHAPpAmzuiarcDRTEE9yddUu8j7EbKYJJ5pB

Merkle Root

39d14bd240608611628e27b962d0fb8c80495b021ebae5551feb8d30eab9e64a

Transactions (1)

Coinbase39d14bd2406086…eb8d30eab9e64a

1 in → 1 out10.0600 XPM109 B

APpAmzui…bKYJJ5pB

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.

3.045 × 10⁹¹(92-digit number)

30456750082141006647…80498443257620947939

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

3.045 × 10⁹¹(92-digit number)

30456750082141006647…80498443257620947939

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.091 × 10⁹¹(92-digit number)

60913500164282013294…60996886515241895879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.218 × 10⁹²(93-digit number)

12182700032856402658…21993773030483791759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.436 × 10⁹²(93-digit number)

24365400065712805317…43987546060967583519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.873 × 10⁹²(93-digit number)

48730800131425610635…87975092121935167039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.746 × 10⁹²(93-digit number)

97461600262851221270…75950184243870334079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.949 × 10⁹³(94-digit number)

19492320052570244254…51900368487740668159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.898 × 10⁹³(94-digit number)

38984640105140488508…03800736975481336319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.796 × 10⁹³(94-digit number)

77969280210280977016…07601473950962672639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.559 × 10⁹⁴(95-digit number)

15593856042056195403…15202947901925345279

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 #245,103

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