Block #507,567

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/23/2014, 8:00:00 PM · Difficulty 10.8164 · 6,286,788 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6b81cea69508ccaf7a06eea2320fe23caae3adbd440eb06571e58018ea41eca2

View on Chainz ↗

Height

#507,567

Difficulty

10.816427

Transactions

Size

834 B

Version

Bits

0ad10159

Nonce

234,280

Timestamp

4/23/2014, 8:00:00 PM

Confirmations

6,286,788

Merkle Root

b57999b376b13cefcad5a177a2abc082d834acbd4b50073a24efbe2062463e32

Transactions (1)

Coinbaseb57999b376b13c…efbe2062463e32

1 in → 20 out8.5300 XPM743 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe AUbecsVa…i8zo8qRf ATKK7iFz…wZm46KN1

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.

1.818 × 10⁹⁷(98-digit number)

18181500715317122280…42939092940578083679

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

1.818 × 10⁹⁷(98-digit number)

18181500715317122280…42939092940578083679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.636 × 10⁹⁷(98-digit number)

36363001430634244561…85878185881156167359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.272 × 10⁹⁷(98-digit number)

72726002861268489123…71756371762312334719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.454 × 10⁹⁸(99-digit number)

14545200572253697824…43512743524624669439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.909 × 10⁹⁸(99-digit number)

29090401144507395649…87025487049249338879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.818 × 10⁹⁸(99-digit number)

58180802289014791299…74050974098498677759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.163 × 10⁹⁹(100-digit number)

11636160457802958259…48101948196997355519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.327 × 10⁹⁹(100-digit number)

23272320915605916519…96203896393994711039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.654 × 10⁹⁹(100-digit number)

46544641831211833039…92407792787989422079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.308 × 10⁹⁹(100-digit number)

93089283662423666078…84815585575978844159

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