Block #250,620

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/8/2013, 2:31:04 PM · Difficulty 9.9686 · 6,545,504 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

eb4c47ec173390829d568bce20439e91fb3c1ffa7490ebea6c37d7a6a223f47e

View on Chainz ↗

Height

#250,620

Difficulty

9.968629

Transactions

Size

1.91 KB

Version

Bits

09f7f81a

Nonce

145,489

Timestamp

11/8/2013, 2:31:04 PM

Confirmations

6,545,504

Mined by

⛏️ aR|cHAKXeSXzuNp3rXfbvqBPuAUeHUgyeuNjvhB

Merkle Root

5f260880aa92ac0c14fad134e4718e01d3f5946c776e26c17fcb5f041b9aaeac

Transactions (1)

Coinbase5f260880aa92ac…cb5f041b9aaeac

1 in → 53 out10.0300 XPM1.82 KB

AKXeSXzu…yeuNjvhB AdL4ZZDR…2eQtg1T9 ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY

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.

5.969 × 10⁸⁸(89-digit number)

59695801409078139714…36251559395685526799

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

5.969 × 10⁸⁸(89-digit number)

59695801409078139714…36251559395685526799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.193 × 10⁸⁹(90-digit number)

11939160281815627942…72503118791371053599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.387 × 10⁸⁹(90-digit number)

23878320563631255885…45006237582742107199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.775 × 10⁸⁹(90-digit number)

47756641127262511771…90012475165484214399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.551 × 10⁸⁹(90-digit number)

95513282254525023542…80024950330968428799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.910 × 10⁹⁰(91-digit number)

19102656450905004708…60049900661936857599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.820 × 10⁹⁰(91-digit number)

38205312901810009417…20099801323873715199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.641 × 10⁹⁰(91-digit number)

76410625803620018834…40199602647747430399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.528 × 10⁹¹(92-digit number)

15282125160724003766…80399205295494860799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.056 × 10⁹¹(92-digit number)

30564250321448007533…60798410590989721599

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