Block #270,970

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/24/2013, 8:16:56 AM · Difficulty 9.9515 · 6,539,966 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

87a25f03c91a70cde1ef52044e4f6d184d609b40edd59a5a18528873de131121

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Height

#270,970

Difficulty

9.951474

Transactions

Size

1.07 KB

Version

Bits

09f393d0

Nonce

133,311

Timestamp

11/24/2013, 8:16:56 AM

Confirmations

6,539,966

Mined by

⛏️ P2SHAZeU2g2L3DVc23NKBGDPLkL6PBm694WpGV

Merkle Root

17343cc593066fabeba4028265a2f4ed2fa7021adf79556f1df10d89a549e784

Transactions (3)

Coinbase80576db96aa7a0…f41163deb2f674

1 in → 1 out10.1000 XPM109 B

AZeU2g2L…m694WpGV

0dc09460264a71…34e9cd698fd578

1 in → 2 out5.0798 XPM227 B

AWhqddAm…5ggySXwy AaJGWm25…f86Ta9oh

5cabf5375f9d31…14de158fe26c2a

4 in → 2 out1.6204 XPM668 B

AVt74fkR…i9NuXag7 AQVsgf7p…yu9hwQNx

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.

3.130 × 10⁹¹(92-digit number)

31307539872849670965…45906090248023868161

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

3.130 × 10⁹¹(92-digit number)

31307539872849670965…45906090248023868161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.261 × 10⁹¹(92-digit number)

62615079745699341930…91812180496047736321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.252 × 10⁹²(93-digit number)

12523015949139868386…83624360992095472641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.504 × 10⁹²(93-digit number)

25046031898279736772…67248721984190945281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.009 × 10⁹²(93-digit number)

50092063796559473544…34497443968381890561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.001 × 10⁹³(94-digit number)

10018412759311894708…68994887936763781121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.003 × 10⁹³(94-digit number)

20036825518623789417…37989775873527562241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.007 × 10⁹³(94-digit number)

40073651037247578835…75979551747055124481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.014 × 10⁹³(94-digit number)

80147302074495157671…51959103494110248961

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 #270,970

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