Block #239,627

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/2/2013, 5:28:20 AM · Difficulty 9.9545 · 6,559,160 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

47a0580602b072e0fdad79494cbc2abb86eb4db90126ad684633a493affd29dd

View on Chainz ↗

Height

#239,627

Difficulty

9.954543

Transactions

Size

1.97 KB

Version

Bits

09f45cf0

Nonce

46,533

Timestamp

11/2/2013, 5:28:20 AM

Confirmations

6,559,160

Mined by

⛏️ RtAWZb1hL4JtNJXmB8RiXjR1EX4p63wEkMsn

Merkle Root

b529691dcb5f188ebbe7daf915512cc6e6cc1ab8a7ee7db08cf5f4cf3bdb9d12

Transactions (1)

Coinbaseb529691dcb5f18…f5f4cf3bdb9d12

1 in → 55 out10.0600 XPM1.89 KB

AWZb1hL4…63wEkMsn AbeUZSvK…ijGzuyjz ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AcMPa5Yh…j5yHgkwm

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.

9.556 × 10⁸⁹(90-digit number)

95567255984965398817…34883373847751541861

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

9.556 × 10⁸⁹(90-digit number)

95567255984965398817…34883373847751541861

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.911 × 10⁹⁰(91-digit number)

19113451196993079763…69766747695503083721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.822 × 10⁹⁰(91-digit number)

38226902393986159527…39533495391006167441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.645 × 10⁹⁰(91-digit number)

76453804787972319054…79066990782012334881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.529 × 10⁹¹(92-digit number)

15290760957594463810…58133981564024669761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.058 × 10⁹¹(92-digit number)

30581521915188927621…16267963128049339521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.116 × 10⁹¹(92-digit number)

61163043830377855243…32535926256098679041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.223 × 10⁹²(93-digit number)

12232608766075571048…65071852512197358081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.446 × 10⁹²(93-digit number)

24465217532151142097…30143705024394716161

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