Block #274,097

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/26/2013, 3:39:38 AM · Difficulty 9.9564 · 6,539,957 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

3c1522a28fddcd769a15d646f736d108a8a26a2aa148df14e66c5832da8f0c7a

View on Chainz ↗

Height

#274,097

Difficulty

9.956356

Transactions

Size

1.04 KB

Version

Bits

09f4d3be

Nonce

198,979

Timestamp

11/26/2013, 3:39:38 AM

Confirmations

6,539,957

Mined by

⛏️ .aRAQNtLvGoDmijMR9NZkenmAQpfspbN1uwGP

Merkle Root

b5604a3c1cb7a4f35618e81b45383266a98362c4a3d6f3fb273886fe8b31965a

Transactions (1)

Coinbaseb5604a3c1cb7a4…3886fe8b31965a

1 in → 27 out10.0700 XPM981 B

AQNtLvGo…pbN1uwGP AX6xJioT…NymntK8m ARkHWBbk…NFGu7Vm7 APVGazMT…cDCk2nwA ARYnzc2o…oDhhtZPZ

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.

5.716 × 10⁹²(93-digit number)

57162483757136385182…83965176876987016699

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

5.716 × 10⁹²(93-digit number)

57162483757136385182…83965176876987016699

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.143 × 10⁹³(94-digit number)

11432496751427277036…67930353753974033399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.286 × 10⁹³(94-digit number)

22864993502854554072…35860707507948066799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.572 × 10⁹³(94-digit number)

45729987005709108145…71721415015896133599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.145 × 10⁹³(94-digit number)

91459974011418216291…43442830031792267199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.829 × 10⁹⁴(95-digit number)

18291994802283643258…86885660063584534399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.658 × 10⁹⁴(95-digit number)

36583989604567286516…73771320127169068799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.316 × 10⁹⁴(95-digit number)

73167979209134573033…47542640254338137599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.463 × 10⁹⁵(96-digit number)

14633595841826914606…95085280508676275199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #274,097

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