Block #57,029

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/17/2013, 11:44:38 AM · Difficulty 8.9523 · 6,737,045 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7086c1be718344542931165bcc5535aa7a4b3ca0be898e952ee6680420500cfc

View on Chainz ↗

Height

#57,029

Difficulty

8.952273

Transactions

Size

9.18 KB

Version

Bits

08f3c82e

Nonce

189

Timestamp

7/17/2013, 11:44:38 AM

Confirmations

6,737,045

Merkle Root

f6fe60abce1ced985a7355c40b63394c6e3c3ce045f1208c002a09dcb87bde46

Transactions (2)

Coinbaseec8aed87f1fe68…651a6487c6c1da

1 in → 1 out12.5600 XPM110 B

ARrp979g…WbMYRi4N

a90034bde72d37…5279558b57f53b

80 in → 2 out1004.9200 XPM8.99 KB

ANBGBvzR…CgPGtqfX ANWeVPrA…5E3WiW79

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.

1.347 × 10⁹³(94-digit number)

13472515125570117315…04543286923178127241

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

1.347 × 10⁹³(94-digit number)

13472515125570117315…04543286923178127241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.694 × 10⁹³(94-digit number)

26945030251140234631…09086573846356254481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.389 × 10⁹³(94-digit number)

53890060502280469262…18173147692712508961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.077 × 10⁹⁴(95-digit number)

10778012100456093852…36346295385425017921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.155 × 10⁹⁴(95-digit number)

21556024200912187705…72692590770850035841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.311 × 10⁹⁴(95-digit number)

43112048401824375410…45385181541700071681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.622 × 10⁹⁴(95-digit number)

86224096803648750820…90770363083400143361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.724 × 10⁹⁵(96-digit number)

17244819360729750164…81540726166800286721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.448 × 10⁹⁵(96-digit number)

34489638721459500328…63081452333600573441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.897 × 10⁹⁵(96-digit number)

68979277442919000656…26162904667201146881

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer