Block #19,659

1CCLength 7★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/12/2013, 9:38:36 AM · Difficulty 7.9243 · 6,776,828 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

72c5a60bca1466b2a0aaa9bf2c3e681d9d48977b74a3c41663024e6966eb780c

View on Chainz ↗

Height

#19,659

Difficulty

7.924283

Transactions

Size

466 B

Version

Bits

07ec9dce

Nonce

497

Timestamp

7/12/2013, 9:38:36 AM

Confirmations

6,776,828

Mined by

⛏️ P2SHANU9e2MbtcX82b8Xki3JtDkxwAtnatsUu7

Merkle Root

8bb8d513c7961599446e22dd518c1d211b0867a7c3b7e604939dafb5589661f0

Transactions (2)

Coinbased9ba6fd992d862…fa2423df74437c

1 in → 1 out15.9100 XPM108 B

ANU9e2Mb…tnatsUu7

5ad12e7029be17…286b5bd4c46c47

2 in → 1 out32.4700 XPM271 B

AU4AxAzL…y8DH19oQ

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.

2.810 × 10⁸⁷(88-digit number)

28106794724226771761…28036309697803320859

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

2.810 × 10⁸⁷(88-digit number)

28106794724226771761…28036309697803320859

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.621 × 10⁸⁷(88-digit number)

56213589448453543523…56072619395606641719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.124 × 10⁸⁸(89-digit number)

11242717889690708704…12145238791213283439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.248 × 10⁸⁸(89-digit number)

22485435779381417409…24290477582426566879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.497 × 10⁸⁸(89-digit number)

44970871558762834818…48580955164853133759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.994 × 10⁸⁸(89-digit number)

89941743117525669637…97161910329706267519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.798 × 10⁸⁹(90-digit number)

17988348623505133927…94323820659412535039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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

CommonChain length 7

Found in most blocks. The baseline for Primecoin's proof-of-work.

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