Block #262,171

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/16/2013, 1:44:41 PM · Difficulty 9.9696 · 6,530,194 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

36cf73f6be77f3c08082f8b016592b7ed8b96068b44c3a6f92f51c7791fabf5d

View on Chainz ↗

Height

#262,171

Difficulty

9.969559

Transactions

Size

1.71 KB

Version

Bits

09f834fe

Nonce

517,978

Timestamp

11/16/2013, 1:44:41 PM

Confirmations

6,530,194

Merkle Root

4e8d16ab0628328fb7aa42932eaa78fe320d67b14275bd0ebc3927c571141cf4

Transactions (1)

Coinbase4e8d16ab062832…3927c571141cf4

1 in → 47 out10.0300 XPM1.62 KB

APZy8y6E…QZaGQjfp AFqKfjez…qX9Ace3g AKXeSXzu…yeuNjvhB APfbVzNM…GWk2KPXG AQtzUSwq…htAuF3yC

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.

6.327 × 10⁹²(93-digit number)

63274655572123070896…07179310519759347199

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

6.327 × 10⁹²(93-digit number)

63274655572123070896…07179310519759347199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.265 × 10⁹³(94-digit number)

12654931114424614179…14358621039518694399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.530 × 10⁹³(94-digit number)

25309862228849228358…28717242079037388799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.061 × 10⁹³(94-digit number)

50619724457698456716…57434484158074777599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.012 × 10⁹⁴(95-digit number)

10123944891539691343…14868968316149555199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.024 × 10⁹⁴(95-digit number)

20247889783079382686…29737936632299110399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.049 × 10⁹⁴(95-digit number)

40495779566158765373…59475873264598220799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.099 × 10⁹⁴(95-digit number)

80991559132317530747…18951746529196441599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.619 × 10⁹⁵(96-digit number)

16198311826463506149…37903493058392883199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.239 × 10⁹⁵(96-digit number)

32396623652927012298…75806986116785766399

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