Block #326,972

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/24/2013, 5:18:42 AM · Difficulty 10.1804 · 6,476,589 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

bed71e373c8ecf9d084d9653050d3dcac8fca007ef91a25a13b51820ba74c46f

View on Chainz ↗

Height

#326,972

Difficulty

10.180360

Transactions

Size

1.01 KB

Version

Bits

0a2e2c15

Nonce

27,017

Timestamp

12/24/2013, 5:18:42 AM

Confirmations

6,476,589

Mined by

⛏️ <aRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

c6ce29035d05c9955417318fa5f767e349769f819e3b23ad8480887bfce7168d

Transactions (1)

Coinbasec6ce29035d05c9…80887bfce7168d

1 in → 26 out9.6293 XPM947 B

Aac9Hjdg…P4ktypc3 AJzWx2VD…j4ZSMit5 AG5YAjec…VhA4Aeh1 AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz

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.

8.821 × 10⁹²(93-digit number)

88211724893224016651…62681639500537433281

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

8.821 × 10⁹²(93-digit number)

88211724893224016651…62681639500537433281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.764 × 10⁹³(94-digit number)

17642344978644803330…25363279001074866561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.528 × 10⁹³(94-digit number)

35284689957289606660…50726558002149733121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.056 × 10⁹³(94-digit number)

70569379914579213321…01453116004299466241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.411 × 10⁹⁴(95-digit number)

14113875982915842664…02906232008598932481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.822 × 10⁹⁴(95-digit number)

28227751965831685328…05812464017197864961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.645 × 10⁹⁴(95-digit number)

56455503931663370657…11624928034395729921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.129 × 10⁹⁵(96-digit number)

11291100786332674131…23249856068791459841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.258 × 10⁹⁵(96-digit number)

22582201572665348262…46499712137582919681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.516 × 10⁹⁵(96-digit number)

45164403145330696525…92999424275165839361

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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