Block #295,040

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/5/2013, 5:42:40 AM · Difficulty 9.9912 · 6,515,050 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b0535c78db905aebce877543ccb8b3d1c6dd7e4e4c27fc11fbfaf021f2b5d023

View on Chainz ↗

Height

#295,040

Difficulty

9.991203

Transactions

Size

1.21 KB

Version

Bits

09fdbf7f

Nonce

15,486

Timestamp

12/5/2013, 5:42:40 AM

Confirmations

6,515,050

Mined by

⛏️ aRF^APeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

e0821950354f240214650e0045f61506c8c7d1676aecd8d57b614ed93b4caa81

Transactions (1)

Coinbasee0821950354f24…614ed93b4caa81

1 in → 32 out9.9800 XPM1.12 KB

APeshfYV…3PKcKMKH ARcqMJhp…RVLToQ6S AWuSjViu…6ogxMMq6 AHuJ9wYh…BGmgHrKZ AX2VaXup…gXWCNRYT

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.

1.610 × 10⁹³(94-digit number)

16107111369754485718…70685245779244813599

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

1.610 × 10⁹³(94-digit number)

16107111369754485718…70685245779244813599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.221 × 10⁹³(94-digit number)

32214222739508971437…41370491558489627199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.442 × 10⁹³(94-digit number)

64428445479017942874…82740983116979254399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.288 × 10⁹⁴(95-digit number)

12885689095803588574…65481966233958508799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.577 × 10⁹⁴(95-digit number)

25771378191607177149…30963932467917017599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.154 × 10⁹⁴(95-digit number)

51542756383214354299…61927864935834035199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.030 × 10⁹⁵(96-digit number)

10308551276642870859…23855729871668070399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.061 × 10⁹⁵(96-digit number)

20617102553285741719…47711459743336140799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.123 × 10⁹⁵(96-digit number)

41234205106571483439…95422919486672281599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.246 × 10⁹⁵(96-digit number)

82468410213142966879…90845838973344563199

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

Block #295,040

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