Block #74,350

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/21/2013, 10:38:05 AM · Difficulty 8.9955 · 6,719,822 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f24f127b3358e498c1f851fe02d4d5e50dafb7ee71899c883060900bc6508478

View on Chainz ↗

Height

#74,350

Difficulty

8.995452

Transactions

Size

199 B

Version

Bits

08fed5ee

Nonce

282

Timestamp

7/21/2013, 10:38:05 AM

Confirmations

6,719,822

Merkle Root

6a2d29e742c87ad339c9c50378304e268a2701a7cd0217cb5424e482a39c1f3c

Transactions (1)

Coinbase6a2d29e742c87a…24e482a39c1f3c

1 in → 1 out12.3400 XPM110 B

AVQxbFsH…KG2vYXbz

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.

1.750 × 10⁹²(93-digit number)

17501400690129043648…36198019740054409249

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

1.750 × 10⁹²(93-digit number)

17501400690129043648…36198019740054409249

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.500 × 10⁹²(93-digit number)

35002801380258087296…72396039480108818499

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.000 × 10⁹²(93-digit number)

70005602760516174593…44792078960217636999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.400 × 10⁹³(94-digit number)

14001120552103234918…89584157920435273999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.800 × 10⁹³(94-digit number)

28002241104206469837…79168315840870547999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.600 × 10⁹³(94-digit number)

56004482208412939674…58336631681741095999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.120 × 10⁹⁴(95-digit number)

11200896441682587934…16673263363482191999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.240 × 10⁹⁴(95-digit number)

22401792883365175869…33346526726964383999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.480 × 10⁹⁴(95-digit number)

44803585766730351739…66693053453928767999

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