Block #263,546

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/17/2013, 10:19:45 PM · Difficulty 9.9659 · 6,532,409 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3ad00543a54064498362dd2133bbd1cbee65ad952487f1dee6712349827c386b

View on Chainz ↗

Height

#263,546

Difficulty

9.965882

Transactions

Size

1.98 KB

Version

Bits

09f74409

Nonce

7,378

Timestamp

11/17/2013, 10:19:45 PM

Confirmations

6,532,409

Mined by

⛏️ zaR@^AeNjg8HA2JzrdQD3LcJMTkwYEE9AkdpcSC

Merkle Root

6f91da24a030b4fac58c05cdb27eab59a3124ff44b3d9fb186e3bb30b188d49d

Transactions (1)

Coinbase6f91da24a030b4…e3bb30b188d49d

1 in → 55 out10.0300 XPM1.89 KB

AeNjg8HA…9AkdpcSC AFqKfjez…qX9Ace3g AQtzUSwq…htAuF3yC APZy8y6E…QZaGQjfp ALSiuDiS…WqQxGQSY

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.

7.613 × 10⁹⁸(99-digit number)

76130485295159160593…78951190794540138241

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

7.613 × 10⁹⁸(99-digit number)

76130485295159160593…78951190794540138241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.522 × 10⁹⁹(100-digit number)

15226097059031832118…57902381589080276481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.045 × 10⁹⁹(100-digit number)

30452194118063664237…15804763178160552961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.090 × 10⁹⁹(100-digit number)

60904388236127328475…31609526356321105921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.218 × 10¹⁰⁰(101-digit number)

12180877647225465695…63219052712642211841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.436 × 10¹⁰⁰(101-digit number)

24361755294450931390…26438105425284423681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.872 × 10¹⁰⁰(101-digit number)

48723510588901862780…52876210850568847361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.744 × 10¹⁰⁰(101-digit number)

97447021177803725560…05752421701137694721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.948 × 10¹⁰¹(102-digit number)

19489404235560745112…11504843402275389441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.897 × 10¹⁰¹(102-digit number)

38978808471121490224…23009686804550778881

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