Block #264,474

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/18/2013, 5:30:35 PM · Difficulty 9.9644 · 6,528,717 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

21358d352eba42758067c31d82c043e7ade0c4cc7e1a2100fc2915763d9a4271

View on Chainz ↗

Height

#264,474

Difficulty

9.964389

Transactions

Size

1.91 KB

Version

Bits

09f6e237

Nonce

98,808

Timestamp

11/18/2013, 5:30:35 PM

Confirmations

6,528,717

Merkle Root

6583327b7542a73f8222b358c281cdcb5254ae049533d8bf4a294c692fc4ef6c

Transactions (1)

Coinbase6583327b7542a7…294c692fc4ef6c

1 in → 53 out10.0400 XPM1.82 KB

AJBcbz2C…z57JquCp AFqKfjez…qX9Ace3g APfZjrNu…Wvzt6AFp ASk3VNLy…13sqXPzG APZy8y6E…QZaGQjfp

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.

2.630 × 10⁹³(94-digit number)

26305519132304587035…14708977196924538799

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

2.630 × 10⁹³(94-digit number)

26305519132304587035…14708977196924538799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.261 × 10⁹³(94-digit number)

52611038264609174071…29417954393849077599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.052 × 10⁹⁴(95-digit number)

10522207652921834814…58835908787698155199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.104 × 10⁹⁴(95-digit number)

21044415305843669628…17671817575396310399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.208 × 10⁹⁴(95-digit number)

42088830611687339256…35343635150792620799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.417 × 10⁹⁴(95-digit number)

84177661223374678513…70687270301585241599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.683 × 10⁹⁵(96-digit number)

16835532244674935702…41374540603170483199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.367 × 10⁹⁵(96-digit number)

33671064489349871405…82749081206340966399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.734 × 10⁹⁵(96-digit number)

67342128978699742811…65498162412681932799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.346 × 10⁹⁶(97-digit number)

13468425795739948562…30996324825363865599

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer