Block #248,688

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/7/2013, 12:53:03 PM · Difficulty 9.9660 · 6,596,214 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

1db72532b099c01ceee85f8f866d9785a12b14fd2d2ec024037544659d251c81

View on Chainz ↗

Height

#248,688

Difficulty

9.966009

Transactions

Size

797 B

Version

Bits

09f74c65

Nonce

6,792

Timestamp

11/7/2013, 12:53:03 PM

Confirmations

6,596,214

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

cbaacb27a8ceaa8ca9ad1407b912e81a9fe7741967652cdcc386862e9a250913

Transactions (3)

Coinbase140159642c5426…b17310a9ef0fc7

1 in → 2 out10.0700 XPM141 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

55901d65c4baf3…98f2cc9163a079

1 in → 1 out10.0500 XPM193 B

AREJRekG…a8dWbE8j

d6fa948a2dbbdb…602dcb4648a3ca

2 in → 2 out10.7012 XPM373 B

ASuoUi24…FwBoFbxd APaASrec…jVQcnoXw

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.

1.546 × 10⁹⁴(95-digit number)

15467475970867174094…23382612974505069499

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

1.546 × 10⁹⁴(95-digit number)

15467475970867174094…23382612974505069499

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.093 × 10⁹⁴(95-digit number)

30934951941734348188…46765225949010138999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.186 × 10⁹⁴(95-digit number)

61869903883468696376…93530451898020277999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.237 × 10⁹⁵(96-digit number)

12373980776693739275…87060903796040555999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.474 × 10⁹⁵(96-digit number)

24747961553387478550…74121807592081111999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.949 × 10⁹⁵(96-digit number)

49495923106774957101…48243615184162223999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.899 × 10⁹⁵(96-digit number)

98991846213549914202…96487230368324447999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.979 × 10⁹⁶(97-digit number)

19798369242709982840…92974460736648895999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.959 × 10⁹⁶(97-digit number)

39596738485419965680…85948921473297791999

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 #248,688

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