Block #1,684,483

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/22/2016, 8:55:54 AM · Difficulty 10.7237 · 5,118,795 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

369d877c056f6220839a44621a6b73c0bba6096008b72ecb119f152dd3d06bd8

View on Chainz ↗

Height

#1,684,483

Difficulty

10.723680

Transactions

Size

425 B

Version

Bits

0ab94313

Nonce

1,075,308,679

Timestamp

7/22/2016, 8:55:54 AM

Confirmations

5,118,795

Mined by

⛏️ P2SHAbKiFTdQkASJPMLuPKARyMnWigqf6cym9P

Merkle Root

29b6dc7a1900af99f593962c73b2130bce1990b6cdaaef3b6250e7c2d4d616b4

Transactions (2)

Coinbase06269210196020…6040867390b37e

1 in → 1 out8.6900 XPM110 B

AbKiFTdQ…qf6cym9P

52e0c7d70d4ccb…423cb929fa2d97

1 in → 2 out8131.2972 XPM225 B

AQcPY7Rn…z9JookEb AWbVLQFv…NfYzWqWQ

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.

2.548 × 10⁹⁴(95-digit number)

25488365795256204572…08965622245743626621

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

2.548 × 10⁹⁴(95-digit number)

25488365795256204572…08965622245743626621

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.097 × 10⁹⁴(95-digit number)

50976731590512409144…17931244491487253241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.019 × 10⁹⁵(96-digit number)

10195346318102481828…35862488982974506481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.039 × 10⁹⁵(96-digit number)

20390692636204963657…71724977965949012961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.078 × 10⁹⁵(96-digit number)

40781385272409927315…43449955931898025921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.156 × 10⁹⁵(96-digit number)

81562770544819854631…86899911863796051841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.631 × 10⁹⁶(97-digit number)

16312554108963970926…73799823727592103681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.262 × 10⁹⁶(97-digit number)

32625108217927941852…47599647455184207361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.525 × 10⁹⁶(97-digit number)

65250216435855883704…95199294910368414721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.305 × 10⁹⁷(98-digit number)

13050043287171176740…90398589820736829441

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