Block #294,893

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/5/2013, 3:28:16 AM · Difficulty 9.9912 · 6,515,194 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f848f79dc6fe381ebdc2412437be9fc06a1074dfc65970eeb4622180f6820685

View on Chainz ↗

Height

#294,893

Difficulty

9.991177

Transactions

Size

1.05 KB

Version

Bits

09fdbdce

Nonce

55,170

Timestamp

12/5/2013, 3:28:16 AM

Confirmations

6,515,194

Mined by

⛏️ aRAFwkgHkaFBj8HDFm6mAfRt6v8ht2vHGx2i

Merkle Root

d25fc9dd51952f707fd142828d87928f9790f4442955efa2af792b1c0c16d55b

Transactions (1)

Coinbased25fc9dd51952f…792b1c0c16d55b

1 in → 27 out10.0000 XPM981 B

AFwkgHka…t2vHGx2i AJzWx2VD…j4ZSMit5 ASLqdKi2…VhTmrwFv AdeRsD79…yxiKThfi AP35Ee6p…Bd7bVK32

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.

2.164 × 10⁹⁴(95-digit number)

21640168904838793032…14368404719891583999

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

2.164 × 10⁹⁴(95-digit number)

21640168904838793032…14368404719891583999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.328 × 10⁹⁴(95-digit number)

43280337809677586064…28736809439783167999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.656 × 10⁹⁴(95-digit number)

86560675619355172129…57473618879566335999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.731 × 10⁹⁵(96-digit number)

17312135123871034425…14947237759132671999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.462 × 10⁹⁵(96-digit number)

34624270247742068851…29894475518265343999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.924 × 10⁹⁵(96-digit number)

69248540495484137703…59788951036530687999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.384 × 10⁹⁶(97-digit number)

13849708099096827540…19577902073061375999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.769 × 10⁹⁶(97-digit number)

27699416198193655081…39155804146122751999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.539 × 10⁹⁶(97-digit number)

55398832396387310162…78311608292245503999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.107 × 10⁹⁷(98-digit number)

11079766479277462032…56623216584491007999

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

Block #294,893

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