Block #245,406

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/5/2013, 10:56:40 AM · Difficulty 9.9639 · 6,591,269 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3b8f007e90fe30f35ee2fd75e909bcc59ef4ae1048c4cc85fedf43c192f86219

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Height

#245,406

Difficulty

9.963878

Transactions

Size

232 B

Version

Bits

09f6c0b8

Nonce

9,372

Timestamp

11/5/2013, 10:56:40 AM

Confirmations

6,591,269

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

284765a090663c3ea8e794ee5ce2d8b8db7f90b44e00c5492b2566b41303ed35

Transactions (1)

Coinbase284765a090663c…2566b41303ed35

1 in → 2 out10.0600 XPM142 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

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.

1.754 × 10⁹⁴(95-digit number)

17545552505431612579…72410783910132990551

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

1.754 × 10⁹⁴(95-digit number)

17545552505431612579…72410783910132990551

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.509 × 10⁹⁴(95-digit number)

35091105010863225159…44821567820265981101

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.018 × 10⁹⁴(95-digit number)

70182210021726450318…89643135640531962201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.403 × 10⁹⁵(96-digit number)

14036442004345290063…79286271281063924401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.807 × 10⁹⁵(96-digit number)

28072884008690580127…58572542562127848801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.614 × 10⁹⁵(96-digit number)

56145768017381160254…17145085124255697601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.122 × 10⁹⁶(97-digit number)

11229153603476232050…34290170248511395201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.245 × 10⁹⁶(97-digit number)

22458307206952464101…68580340497022790401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.491 × 10⁹⁶(97-digit number)

44916614413904928203…37160680994045580801

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #245,406

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