Block #249,770

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/8/2013, 3:44:40 AM · Difficulty 9.9673 · 6,549,267 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

41a6730edda9d6eddd1c1bf7bfc1364e9013dc7604d668c5e8dd19421cb4e773

View on Chainz ↗

Height

#249,770

Difficulty

9.967305

Transactions

Size

1.10 KB

Version

Bits

09f7a152

Nonce

10,060

Timestamp

11/8/2013, 3:44:40 AM

Confirmations

6,549,267

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

d6ee6c85c283c47f659dd28a73fa9e54fe14d29d11384180761c766a7b2252df

Transactions (3)

Coinbase83bf8dc10259c2…764c7b5a55c339

1 in → 2 out10.0700 XPM136 B

AZDUEbdS…RYKMRZET ALfEGCwh…VawujfMm

353a47add16e7b…94b2dbe5e63f32

2 in → 2 out51.9485 XPM375 B

Acc4rFoA…PircGcM5 AHFCEs3o…Pbs9VA6g

d1a1f3c5efe905…a39663786c075a

3 in → 2 out9.6390 XPM522 B

ATPyhKCX…8PqhPNZD AGaKkABV…XGSDBNzn

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.

5.144 × 10⁹⁴(95-digit number)

51448908165404131322…91565275988603304399

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

5.144 × 10⁹⁴(95-digit number)

51448908165404131322…91565275988603304399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.028 × 10⁹⁵(96-digit number)

10289781633080826264…83130551977206608799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.057 × 10⁹⁵(96-digit number)

20579563266161652529…66261103954413217599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.115 × 10⁹⁵(96-digit number)

41159126532323305058…32522207908826435199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.231 × 10⁹⁵(96-digit number)

82318253064646610116…65044415817652870399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.646 × 10⁹⁶(97-digit number)

16463650612929322023…30088831635305740799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.292 × 10⁹⁶(97-digit number)

32927301225858644046…60177663270611481599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.585 × 10⁹⁶(97-digit number)

65854602451717288092…20355326541222963199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.317 × 10⁹⁷(98-digit number)

13170920490343457618…40710653082445926399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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