Block #298,151

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/7/2013, 3:35:34 AM · Difficulty 9.9919 · 6,497,857 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d5534432d1262c4869b833a366c2d35164c29da9e86d8f398940e246d02b01d2

View on Chainz ↗

Height

#298,151

Difficulty

9.991911

Transactions

Size

1.15 KB

Version

Bits

09fdede8

Nonce

66,531

Timestamp

12/7/2013, 3:35:34 AM

Confirmations

6,497,857

Mined by

⛏️ aRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

eb8444ddc5df7ee4c8cc6325c04860aad618d77b03009375bcd8676b27fbdf3d

Transactions (1)

Coinbaseeb8444ddc5df7e…d8676b27fbdf3d

1 in → 30 out9.9800 XPM1.06 KB

Ad9pSzHt…cpJ3y2zz AYcLTeXR…bscgPops AHuJ9wYh…BGmgHrKZ AQyr8Lw3…hs4nt3Pn AdyKWr2A…7PSnFqeJ

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.

7.627 × 10⁹⁵(96-digit number)

76279433865105780426…07200624597465599999

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

7.627 × 10⁹⁵(96-digit number)

76279433865105780426…07200624597465599999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.525 × 10⁹⁶(97-digit number)

15255886773021156085…14401249194931199999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.051 × 10⁹⁶(97-digit number)

30511773546042312170…28802498389862399999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.102 × 10⁹⁶(97-digit number)

61023547092084624341…57604996779724799999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.220 × 10⁹⁷(98-digit number)

12204709418416924868…15209993559449599999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.440 × 10⁹⁷(98-digit number)

24409418836833849736…30419987118899199999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.881 × 10⁹⁷(98-digit number)

48818837673667699473…60839974237798399999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.763 × 10⁹⁷(98-digit number)

97637675347335398946…21679948475596799999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.952 × 10⁹⁸(99-digit number)

19527535069467079789…43359896951193599999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.905 × 10⁹⁸(99-digit number)

39055070138934159578…86719793902387199999

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 First 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 1CC formula:

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

Cross-reference on Chainz Explorer