Block #136,950

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/27/2013, 12:44:19 PM · Difficulty 9.8188 · 6,690,344 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

18247aa8dabb25067415b811aa84af6d5a27308ba1874ea5840b5c99205f007e

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Height

#136,950

Difficulty

9.818795

Transactions

Size

197 B

Version

Bits

09d19c8f

Nonce

119,333

Timestamp

8/27/2013, 12:44:19 PM

Confirmations

6,690,344

Mined by

⛏️ P2SHAetpQsvWbRdpVzLR1MmQMvbogyBEePeKKm

Merkle Root

bbc4b989a0b21d1a2b425d46434d6e9dd1947b9bbd8f02e18c7007f0951282fc

Transactions (1)

Coinbasebbc4b989a0b21d…7007f0951282fc

1 in → 1 out10.3600 XPM109 B

AetpQsvW…BEePeKKm

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.

2.444 × 10⁹⁰(91-digit number)

24447272257056409150…27544803418895204481

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

2.444 × 10⁹⁰(91-digit number)

24447272257056409150…27544803418895204481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.889 × 10⁹⁰(91-digit number)

48894544514112818301…55089606837790408961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.778 × 10⁹⁰(91-digit number)

97789089028225636603…10179213675580817921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.955 × 10⁹¹(92-digit number)

19557817805645127320…20358427351161635841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.911 × 10⁹¹(92-digit number)

39115635611290254641…40716854702323271681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.823 × 10⁹¹(92-digit number)

78231271222580509282…81433709404646543361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.564 × 10⁹²(93-digit number)

15646254244516101856…62867418809293086721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.129 × 10⁹²(93-digit number)

31292508489032203713…25734837618586173441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.258 × 10⁹²(93-digit number)

62585016978064407426…51469675237172346881

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 #136,950

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