Block #302,950

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/10/2013, 2:44:17 AM · Difficulty 9.9929 · 6,503,278 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

52aaf4c1de4f680c135efe333e80b39f918313db0b526bfef90dd13fac4bf5f1

View on Chainz ↗

Height

#302,950

Difficulty

9.992863

Transactions

Size

1.08 KB

Version

Bits

09fe2c44

Nonce

26,767

Timestamp

12/10/2013, 2:44:17 AM

Confirmations

6,503,278

Mined by

⛏️ faROAYcLTeXRXcXHePDnP5p1bevW8AbscgPops

Merkle Root

6b6c133d2cf87a862dac84fc1fc6d2f2fc4d79753d1f270a52a02090ce9e2d48

Transactions (1)

Coinbase6b6c133d2cf87a…a02090ce9e2d48

1 in → 28 out9.9800 XPM1015 B

AYcLTeXR…bscgPops AcABUaNj…WXyu2did AQcxJ4Xd…1kZvMKNx AWtNMiiS…pEccLFSq AQf7sjuh…sNY5fXpu

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.

1.149 × 10⁹⁹(100-digit number)

11490105169517155876…22936940577206785881

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

1.149 × 10⁹⁹(100-digit number)

11490105169517155876…22936940577206785881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.298 × 10⁹⁹(100-digit number)

22980210339034311752…45873881154413571761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.596 × 10⁹⁹(100-digit number)

45960420678068623504…91747762308827143521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.192 × 10⁹⁹(100-digit number)

91920841356137247009…83495524617654287041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.838 × 10¹⁰⁰(101-digit number)

18384168271227449401…66991049235308574081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.676 × 10¹⁰⁰(101-digit number)

36768336542454898803…33982098470617148161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.353 × 10¹⁰⁰(101-digit number)

73536673084909797607…67964196941234296321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.470 × 10¹⁰¹(102-digit number)

14707334616981959521…35928393882468592641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.941 × 10¹⁰¹(102-digit number)

29414669233963919042…71856787764937185281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.882 × 10¹⁰¹(102-digit number)

58829338467927838085…43713575529874370561

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