Block #437,504

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/10/2014, 8:41:46 AM · Difficulty 10.3572 · 6,366,099 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ee4f771fe5948272cc80e779bd8c0fba93df4548a9c87b37f7a6227c53fc5dea

View on Chainz ↗

Height

#437,504

Difficulty

10.357229

Transactions

Size

934 B

Version

Bits

0a5b7358

Nonce

43,734

Timestamp

3/10/2014, 8:41:46 AM

Confirmations

6,366,099

Mined by

⛏️ aSzAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e3f86f197c5ca92ac60d02b6a7d241bc8621abb5fcadecd9a96c2cca66f038c5

Transactions (1)

Coinbasee3f86f197c5ca9…6c2cca66f038c5

1 in → 23 out9.3100 XPM844 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGD4yZQw…hGzM2XAx AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

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.

1.398 × 10⁹⁴(95-digit number)

13989298284898817249…27292339548493518001

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

1.398 × 10⁹⁴(95-digit number)

13989298284898817249…27292339548493518001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.797 × 10⁹⁴(95-digit number)

27978596569797634499…54584679096987036001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.595 × 10⁹⁴(95-digit number)

55957193139595268998…09169358193974072001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.119 × 10⁹⁵(96-digit number)

11191438627919053799…18338716387948144001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.238 × 10⁹⁵(96-digit number)

22382877255838107599…36677432775896288001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.476 × 10⁹⁵(96-digit number)

44765754511676215199…73354865551792576001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.953 × 10⁹⁵(96-digit number)

89531509023352430398…46709731103585152001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.790 × 10⁹⁶(97-digit number)

17906301804670486079…93419462207170304001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.581 × 10⁹⁶(97-digit number)

35812603609340972159…86838924414340608001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.162 × 10⁹⁶(97-digit number)

71625207218681944318…73677848828681216001

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer