Block #227,375

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/25/2013, 8:13:54 PM · Difficulty 9.9367 · 6,571,324 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

1deb129e46c05c2b35fba835dee0fb4bea6ee4508c4e245a48bead4f1099bdfb

View on Chainz ↗

Height

#227,375

Difficulty

9.936695

Transactions

Size

1.18 KB

Version

Bits

09efcb3f

Nonce

2,069

Timestamp

10/25/2013, 8:13:54 PM

Confirmations

6,571,324

Mined by

⛏️ xRjAWxMqAjDsVDnL1kBWfXmRHrWXZjNai1Anq

Merkle Root

ed4f807f83755950543e1e6665d088599128a492c380985a6a0428862fb0c838

Transactions (1)

Coinbaseed4f807f837559…0428862fb0c838

1 in → 31 out10.0900 XPM1.09 KB

AWxMqAjD…jNai1Anq AFqKfjez…qX9Ace3g AGHsFFzK…3J7QNqtQ ANpPrsJp…YzdEphWb AWCfnjpk…hb1ovL8F

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.

1.387 × 10⁹¹(92-digit number)

13871324767493629950…60548813561284339999

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

1.387 × 10⁹¹(92-digit number)

13871324767493629950…60548813561284339999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.774 × 10⁹¹(92-digit number)

27742649534987259900…21097627122568679999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.548 × 10⁹¹(92-digit number)

55485299069974519800…42195254245137359999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.109 × 10⁹²(93-digit number)

11097059813994903960…84390508490274719999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.219 × 10⁹²(93-digit number)

22194119627989807920…68781016980549439999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.438 × 10⁹²(93-digit number)

44388239255979615840…37562033961098879999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.877 × 10⁹²(93-digit number)

88776478511959231680…75124067922197759999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.775 × 10⁹³(94-digit number)

17755295702391846336…50248135844395519999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.551 × 10⁹³(94-digit number)

35510591404783692672…00496271688791039999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.102 × 10⁹³(94-digit number)

71021182809567385344…00992543377582079999

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