Block #528,704

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/6/2014, 7:25:00 PM · Difficulty 10.8880 · 6,264,069 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

976f7a2b3bc89ec60660efcc0b6061d51ea07867142ecb6878cc8c2fbdd9c64e

View on Chainz ↗

Height

#528,704

Difficulty

10.887977

Transactions

Size

731 B

Version

Bits

0ae35278

Nonce

386,721

Timestamp

5/6/2014, 7:25:00 PM

Confirmations

6,264,069

Merkle Root

419b2569ca292d51fa3291b15f091f52f79b231f7604fd7c70cfee9effe2e1ba

Transactions (1)

Coinbase419b2569ca292d…cfee9effe2e1ba

1 in → 17 out8.4200 XPM641 B

ATKK7iFz…wZm46KN1 AdxPNkWD…ZMa9u34q AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AQyr8Lw3…hs4nt3Pn

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.

1.523 × 10⁹⁵(96-digit number)

15232025875553792904…83465896161802777601

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

1.523 × 10⁹⁵(96-digit number)

15232025875553792904…83465896161802777601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.046 × 10⁹⁵(96-digit number)

30464051751107585808…66931792323605555201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.092 × 10⁹⁵(96-digit number)

60928103502215171616…33863584647211110401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.218 × 10⁹⁶(97-digit number)

12185620700443034323…67727169294422220801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.437 × 10⁹⁶(97-digit number)

24371241400886068646…35454338588844441601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.874 × 10⁹⁶(97-digit number)

48742482801772137293…70908677177688883201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.748 × 10⁹⁶(97-digit number)

97484965603544274587…41817354355377766401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.949 × 10⁹⁷(98-digit number)

19496993120708854917…83634708710755532801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.899 × 10⁹⁷(98-digit number)

38993986241417709834…67269417421511065601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.798 × 10⁹⁷(98-digit number)

77987972482835419669…34538834843022131201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.559 × 10⁹⁸(99-digit number)

15597594496567083933…69077669686044262401

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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