Block #532,234

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/8/2014, 11:50:19 PM · Difficulty 10.8963 · 6,292,267 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f0eb537440f807077725b66d20c4bbb3572647c2d20851ab3c4bdcf781d5af02

View on Chainz ↗

Height

#532,234

Difficulty

10.896337

Transactions

Size

834 B

Version

Bits

0ae57650

Nonce

68,132

Timestamp

5/8/2014, 11:50:19 PM

Confirmations

6,292,267

Mined by

AUFKXvnz49HF4GkAnNdcLhTMXs342ApNcm

Merkle Root

7d82f126944dd6376746d4e0cc9e91d622361cccdc241cac33940b52f1fa6938

Transactions (1)

Coinbase7d82f126944dd6…940b52f1fa6938

1 in → 20 out8.4100 XPM743 B

AUFKXvnz…342ApNcm AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH AUDD9tmA…gJPQLnsz Af3sSYhs…KVLY7yAf

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.

1.135 × 10⁹⁷(98-digit number)

11352703242524444599…73928070960056535799

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

1.135 × 10⁹⁷(98-digit number)

11352703242524444599…73928070960056535799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.270 × 10⁹⁷(98-digit number)

22705406485048889198…47856141920113071599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.541 × 10⁹⁷(98-digit number)

45410812970097778397…95712283840226143199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.082 × 10⁹⁷(98-digit number)

90821625940195556794…91424567680452286399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.816 × 10⁹⁸(99-digit number)

18164325188039111358…82849135360904572799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.632 × 10⁹⁸(99-digit number)

36328650376078222717…65698270721809145599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.265 × 10⁹⁸(99-digit number)

72657300752156445435…31396541443618291199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.453 × 10⁹⁹(100-digit number)

14531460150431289087…62793082887236582399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.906 × 10⁹⁹(100-digit number)

29062920300862578174…25586165774473164799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.812 × 10⁹⁹(100-digit number)

58125840601725156348…51172331548946329599

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 #532,234

Cookie Preferences