Block #183,916

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/28/2013, 8:15:48 AM · Difficulty 9.8585 · 6,611,141 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

47685e31b5f95358e43333494d77cb08f8db9b5989f3f6e36c6cdcd699173815

View on Chainz ↗

Height

#183,916

Difficulty

9.858475

Transactions

Size

2.11 KB

Version

Bits

09dbc501

Nonce

1,164,739,828

Timestamp

9/28/2013, 8:15:48 AM

Confirmations

6,611,141

Mined by

⛏️ lRF*ZAPHngwz27GMW45jJC6wSAHExgSoXWG6CFr

Merkle Root

867aabefcef56d1945e5b871f268060c7d7b23de986889cc0a3d52e28c44ca06

Transactions (2)

Coinbase8a9e346d99bdbc…b9d69dc9134ac6

1 in → 23 out10.2900 XPM844 B

APHngwz2…oXWG6CFr AV4rziFj…QhTLsLyZ AKwqFUdz…D4jGNKFN AL7194fk…YNQBVjTB Ac5sZcdP…kzV4eckG

8f7b53037496f1…27aa65f1bc7611

8 in → 2 out11.0239 XPM1.20 KB

AFz9fXym…wh4UqpkL AVNW9aXJ…PYfs4Ypo

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.

1.582 × 10⁹⁴(95-digit number)

15829271864158522893…35859143771332783281

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

1.582 × 10⁹⁴(95-digit number)

15829271864158522893…35859143771332783281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.165 × 10⁹⁴(95-digit number)

31658543728317045786…71718287542665566561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.331 × 10⁹⁴(95-digit number)

63317087456634091572…43436575085331133121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.266 × 10⁹⁵(96-digit number)

12663417491326818314…86873150170662266241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.532 × 10⁹⁵(96-digit number)

25326834982653636629…73746300341324532481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.065 × 10⁹⁵(96-digit number)

50653669965307273258…47492600682649064961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.013 × 10⁹⁶(97-digit number)

10130733993061454651…94985201365298129921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.026 × 10⁹⁶(97-digit number)

20261467986122909303…89970402730596259841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.052 × 10⁹⁶(97-digit number)

40522935972245818606…79940805461192519681

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer