Block #80,445

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/24/2013, 4:03:48 AM · Difficulty 9.2498 · 6,711,900 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

16dfe4ec8aac683e82007c7a2da363b95527d636d028aa32be66e697bea8a3ed

View on Chainz ↗

Height

#80,445

Difficulty

9.249837

Transactions

Size

884 B

Version

Bits

093ff555

Nonce

289

Timestamp

7/24/2013, 4:03:48 AM

Confirmations

6,711,900

Merkle Root

f04ed4a3e80f8fc81746d5ae513e7e471ccce7d91312fe29118381803af749b3

Transactions (2)

Coinbase9903a2f6e70ca6…b3ccb96e685388

1 in → 1 out11.6800 XPM110 B

AdR5q9cb…rWnZwFZ3

806a92a4ba240f…9d2c63b62e4702

5 in → 2 out50.2800 XPM682 B

AMmUy3x3…qPezWtyV AeUPH3ZW…RYivfTCW

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.

1.047 × 10⁹⁹(100-digit number)

10474189861749525049…41172987418036290561

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

1.047 × 10⁹⁹(100-digit number)

10474189861749525049…41172987418036290561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.094 × 10⁹⁹(100-digit number)

20948379723499050099…82345974836072581121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.189 × 10⁹⁹(100-digit number)

41896759446998100199…64691949672145162241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.379 × 10⁹⁹(100-digit number)

83793518893996200399…29383899344290324481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.675 × 10¹⁰⁰(101-digit number)

16758703778799240079…58767798688580648961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.351 × 10¹⁰⁰(101-digit number)

33517407557598480159…17535597377161297921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.703 × 10¹⁰⁰(101-digit number)

67034815115196960319…35071194754322595841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.340 × 10¹⁰¹(102-digit number)

13406963023039392063…70142389508645191681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.681 × 10¹⁰¹(102-digit number)

26813926046078784127…40284779017290383361

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