Block #575,918

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/4/2014, 6:31:20 AM · Difficulty 10.9685 · 6,217,082 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

4d155e8bd63a5b21f0cae13f2d81b042f9791af562828f5caf85eecb2f9c6033

View on Chainz ↗

Height

#575,918

Difficulty

10.968536

Transactions

Size

244 B

Version

Bits

0af7f1fa

Nonce

137,072,782

Timestamp

6/4/2014, 6:31:20 AM

Confirmations

6,217,082

Merkle Root

3401814e487233cfb260b0123ecdaa93634fb0570776c7b9139c399a308bea54

Transactions (1)

Coinbase3401814e487233…9c399a308bea54

1 in → 2 out8.3000 XPM152 B

AXn1KW6P…c7VDu2zv ALPu3s2c…EJXLjVFh

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.

2.621 × 10⁹⁸(99-digit number)

26214864799665983224…40315434262645207519

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

2.621 × 10⁹⁸(99-digit number)

26214864799665983224…40315434262645207519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.242 × 10⁹⁸(99-digit number)

52429729599331966448…80630868525290415039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.048 × 10⁹⁹(100-digit number)

10485945919866393289…61261737050580830079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.097 × 10⁹⁹(100-digit number)

20971891839732786579…22523474101161660159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.194 × 10⁹⁹(100-digit number)

41943783679465573159…45046948202323320319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.388 × 10⁹⁹(100-digit number)

83887567358931146318…90093896404646640639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.677 × 10¹⁰⁰(101-digit number)

16777513471786229263…80187792809293281279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.355 × 10¹⁰⁰(101-digit number)

33555026943572458527…60375585618586562559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.711 × 10¹⁰⁰(101-digit number)

67110053887144917054…20751171237173125119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.342 × 10¹⁰¹(102-digit number)

13422010777428983410…41502342474346250239

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