Block #493,397

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/15/2014, 4:27:59 PM · Difficulty 10.6994 · 6,299,918 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c3cddf6e5c7cc57a94f87398aecbeac291c45925937af629e71b8bb1c2e82715

View on Chainz ↗

Height

#493,397

Difficulty

10.699374

Transactions

Size

989 B

Version

Bits

0ab30a2f

Nonce

17,988,803

Timestamp

4/15/2014, 4:27:59 PM

Confirmations

6,299,918

Merkle Root

8a06ba283eb955e5feee13c5ed457c11ce8b81840b9148c564e5726ddc4cd03f

Transactions (2)

Coinbasee847cedb8f4113…bf2a9b5efad09c

1 in → 1 out8.7300 XPM116 B

AbwWkWZt…kawDhufa

3d0571c0ed7ae7…069867c97f005b

5 in → 1 out6.3223 XPM782 B

Ac8knWXR…uUMyn63E

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.

6.321 × 10⁹⁷(98-digit number)

63210213641486924175…19607905821682897801

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

6.321 × 10⁹⁷(98-digit number)

63210213641486924175…19607905821682897801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.264 × 10⁹⁸(99-digit number)

12642042728297384835…39215811643365795601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.528 × 10⁹⁸(99-digit number)

25284085456594769670…78431623286731591201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.056 × 10⁹⁸(99-digit number)

50568170913189539340…56863246573463182401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.011 × 10⁹⁹(100-digit number)

10113634182637907868…13726493146926364801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.022 × 10⁹⁹(100-digit number)

20227268365275815736…27452986293852729601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.045 × 10⁹⁹(100-digit number)

40454536730551631472…54905972587705459201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.090 × 10⁹⁹(100-digit number)

80909073461103262944…09811945175410918401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.618 × 10¹⁰⁰(101-digit number)

16181814692220652588…19623890350821836801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.236 × 10¹⁰⁰(101-digit number)

32363629384441305177…39247780701643673601

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