Block #294,961

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 12/5/2013, 4:40:24 AM · Difficulty 9.9912 · 6,519,161 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

95947824e60db100549d7d94d0d29a09dc85511281cd8d02d7949f7b0436d7cf

View on Chainz ↗

Height

#294,961

Difficulty

9.991172

Transactions

Size

1.14 KB

Version

Bits

09fdbd77

Nonce

157,835

Timestamp

12/5/2013, 4:40:24 AM

Confirmations

6,519,161

Mined by

⛏️ 1aRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

66e5d0c8d1a38314c48f2547b608af5b6ce0ddf067037bf9004ebd1ef0eca12c

Transactions (1)

Coinbase66e5d0c8d1a383…4ebd1ef0eca12c

1 in → 30 out9.9719 XPM1.06 KB

Ad9pSzHt…cpJ3y2zz AYcLTeXR…bscgPops AY1tyV9E…mJLiTZPS Ae2JNdQB…YBTuYT15 AJjsX4t4…gtmJp9SX

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.

9.020 × 10⁹⁵(96-digit number)

90209391546569481441…64953405679532121599

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

9.020 × 10⁹⁵(96-digit number)

90209391546569481441…64953405679532121599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.804 × 10⁹⁶(97-digit number)

18041878309313896288…29906811359064243199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.608 × 10⁹⁶(97-digit number)

36083756618627792576…59813622718128486399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.216 × 10⁹⁶(97-digit number)

72167513237255585152…19627245436256972799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.443 × 10⁹⁷(98-digit number)

14433502647451117030…39254490872513945599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.886 × 10⁹⁷(98-digit number)

28867005294902234061…78508981745027891199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.773 × 10⁹⁷(98-digit number)

57734010589804468122…57017963490055782399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.154 × 10⁹⁸(99-digit number)

11546802117960893624…14035926980111564799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.309 × 10⁹⁸(99-digit number)

23093604235921787248…28071853960223129599

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 #294,961

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