Block #261,954

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/16/2013, 8:38:50 AM · Difficulty 9.9701 · 6,542,256 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f9763f304f74eb964bafbff3ec9162eed185a11cfdb2fe0999799c407c900820

View on Chainz ↗

Height

#261,954

Difficulty

9.970076

Transactions

Size

1.94 KB

Version

Bits

09f856e8

Nonce

182,487

Timestamp

11/16/2013, 8:38:50 AM

Confirmations

6,542,256

Mined by

⛏️ BaR.YAdWEcK3rEzi97mdrbQ1dKgt3GmHNaeWgVb

Merkle Root

8e8b128a7ca3402c26f3230db6198685b36b8bf2f6d6c98f9df7a60d4fb1fc6d

Transactions (1)

Coinbase8e8b128a7ca340…f7a60d4fb1fc6d

1 in → 54 out10.0300 XPM1.85 KB

AdWEcK3r…HNaeWgVb AFqKfjez…qX9Ace3g APH8rV6F…heb1HF2Z AKXeSXzu…yeuNjvhB AQtzUSwq…htAuF3yC

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.

4.020 × 10⁹²(93-digit number)

40209965682464221777…50185977963917311999

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

4.020 × 10⁹²(93-digit number)

40209965682464221777…50185977963917311999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.041 × 10⁹²(93-digit number)

80419931364928443554…00371955927834623999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.608 × 10⁹³(94-digit number)

16083986272985688710…00743911855669247999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.216 × 10⁹³(94-digit number)

32167972545971377421…01487823711338495999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.433 × 10⁹³(94-digit number)

64335945091942754843…02975647422676991999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.286 × 10⁹⁴(95-digit number)

12867189018388550968…05951294845353983999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.573 × 10⁹⁴(95-digit number)

25734378036777101937…11902589690707967999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.146 × 10⁹⁴(95-digit number)

51468756073554203874…23805179381415935999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.029 × 10⁹⁵(96-digit number)

10293751214710840774…47610358762831871999

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