Block #148,938

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/4/2013, 1:26:44 AM · Difficulty 9.8562 · 6,659,523 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

43af83455bc1fdbb9792cd676a704b7573db615762bf5c9dd02d28b42ef151e1

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Height

#148,938

Difficulty

9.856174

Transactions

Size

200 B

Version

Bits

09db2e34

Nonce

576,012

Timestamp

9/4/2013, 1:26:44 AM

Confirmations

6,659,523

Mined by

⛏️ P2SHAJkcBGvuouoWiEQ4AmFvGo3qwPhSNwhPED

Merkle Root

08733ccf77239471e702911fc3b1e935dd26d08e98f704ebccdff5584d68ec7e

Transactions (1)

Coinbase08733ccf772394…dff5584d68ec7e

1 in → 1 out10.2800 XPM109 B

AJkcBGvu…hSNwhPED

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.

3.002 × 10⁹⁶(97-digit number)

30024456074151368260…75135202697006297601

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

3.002 × 10⁹⁶(97-digit number)

30024456074151368260…75135202697006297601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.004 × 10⁹⁶(97-digit number)

60048912148302736520…50270405394012595201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.200 × 10⁹⁷(98-digit number)

12009782429660547304…00540810788025190401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.401 × 10⁹⁷(98-digit number)

24019564859321094608…01081621576050380801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.803 × 10⁹⁷(98-digit number)

48039129718642189216…02163243152100761601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.607 × 10⁹⁷(98-digit number)

96078259437284378432…04326486304201523201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.921 × 10⁹⁸(99-digit number)

19215651887456875686…08652972608403046401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.843 × 10⁹⁸(99-digit number)

38431303774913751373…17305945216806092801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.686 × 10⁹⁸(99-digit number)

76862607549827502746…34611890433612185601

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 #148,938

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