Block #247,102

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/6/2013, 1:33:15 PM · Difficulty 9.9647 · 6,558,955 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0278067c3b50ad0c27a230c93dad4ab83046f8d279da1b0397056f471c0a40d0

View on Chainz ↗

Height

#247,102

Difficulty

9.964655

Transactions

Size

1.68 KB

Version

Bits

09f6f399

Nonce

8,687

Timestamp

11/6/2013, 1:33:15 PM

Confirmations

6,558,955

Mined by

⛏️ >RzE9APHngwz27GMW45jJC6wSAHExgSoXWG6CFr

Merkle Root

d8bc388dc44a02bf35e859c6ea8a5731a0ea77024ecf5de60ce887469f36bfcd

Transactions (1)

Coinbased8bc388dc44a02…e887469f36bfcd

1 in → 46 out10.0400 XPM1.59 KB

APHngwz2…oXWG6CFr AabHNb1B…GRoingRy AaZDdVPu…hmkbbPfG ARpndEmc…Hg792kEk AXJbpPXX…UowxmF1S

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.

3.117 × 10⁹⁸(99-digit number)

31179972798208915097…42059161953576633599

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

3.117 × 10⁹⁸(99-digit number)

31179972798208915097…42059161953576633599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.235 × 10⁹⁸(99-digit number)

62359945596417830194…84118323907153267199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.247 × 10⁹⁹(100-digit number)

12471989119283566038…68236647814306534399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.494 × 10⁹⁹(100-digit number)

24943978238567132077…36473295628613068799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.988 × 10⁹⁹(100-digit number)

49887956477134264155…72946591257226137599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.977 × 10⁹⁹(100-digit number)

99775912954268528310…45893182514452275199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.995 × 10¹⁰⁰(101-digit number)

19955182590853705662…91786365028904550399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.991 × 10¹⁰⁰(101-digit number)

39910365181707411324…83572730057809100799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.982 × 10¹⁰⁰(101-digit number)

79820730363414822648…67145460115618201599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.596 × 10¹⁰¹(102-digit number)

15964146072682964529…34290920231236403199

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