Block #1,523,837

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/3/2016, 12:40:07 AM · Difficulty 10.6008 · 5,292,823 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

3649216ec73e8dabded5d5d6fd71bf2e8660352e1659697e506745b77ae81437

View on Chainz ↗

Height

#1,523,837

Difficulty

10.600758

Transactions

Size

242 B

Version

Bits

0a99cb43

Nonce

172,542,343

Timestamp

4/3/2016, 12:40:07 AM

Confirmations

5,292,823

Mined by

⛏️ P2SHAQKCdMvyCMWc7q4ViVUJA2RGyaXhCo1gqd

Merkle Root

c2ed74a14cdd9d35dab5b9d38612afbe0593d22ec9e79f305d60e519f947ad56

Transactions (1)

Coinbasec2ed74a14cdd9d…60e519f947ad56

1 in → 2 out8.8800 XPM152 B

AQKCdMvy…XhCo1gqd 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.

2.546 × 10⁹⁵(96-digit number)

25466879250191635803…65080997912620115359

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

2.546 × 10⁹⁵(96-digit number)

25466879250191635803…65080997912620115359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.093 × 10⁹⁵(96-digit number)

50933758500383271606…30161995825240230719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.018 × 10⁹⁶(97-digit number)

10186751700076654321…60323991650480461439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.037 × 10⁹⁶(97-digit number)

20373503400153308642…20647983300960922879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.074 × 10⁹⁶(97-digit number)

40747006800306617285…41295966601921845759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.149 × 10⁹⁶(97-digit number)

81494013600613234570…82591933203843691519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.629 × 10⁹⁷(98-digit number)

16298802720122646914…65183866407687383039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.259 × 10⁹⁷(98-digit number)

32597605440245293828…30367732815374766079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.519 × 10⁹⁷(98-digit number)

65195210880490587656…60735465630749532159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.303 × 10⁹⁸(99-digit number)

13039042176098117531…21470931261499064319

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 #1,523,837

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