Block #1,512,743

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/26/2016, 6:52:59 AM · Difficulty 10.6044 · 5,313,692 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

432dd8e5d1e2118a385533b49b930e1ceeb3c8d5aeca4d9d782d0dca13ffa06b

View on Chainz ↗

Height

#1,512,743

Difficulty

10.604366

Transactions

Size

243 B

Version

Bits

0a9ab7bd

Nonce

2,882,594,843

Timestamp

3/26/2016, 6:52:59 AM

Confirmations

5,313,692

Mined by

⛏️ P2SHAcepRDLodpVcfiX2CCvgEjXGujjKW43xXW

Merkle Root

0145bff97770e1754efc24461778486ba0ff70795c8b839a4c847140d157d6f6

Transactions (1)

Coinbase0145bff97770e1…847140d157d6f6

1 in → 2 out8.8800 XPM152 B

AcepRDLo…jKW43xXW 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.

8.783 × 10⁹⁶(97-digit number)

87837290149112875686…79020552142530746879

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

8.783 × 10⁹⁶(97-digit number)

87837290149112875686…79020552142530746879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.756 × 10⁹⁷(98-digit number)

17567458029822575137…58041104285061493759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.513 × 10⁹⁷(98-digit number)

35134916059645150274…16082208570122987519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.026 × 10⁹⁷(98-digit number)

70269832119290300549…32164417140245975039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.405 × 10⁹⁸(99-digit number)

14053966423858060109…64328834280491950079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.810 × 10⁹⁸(99-digit number)

28107932847716120219…28657668560983900159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.621 × 10⁹⁸(99-digit number)

56215865695432240439…57315337121967800319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.124 × 10⁹⁹(100-digit number)

11243173139086448087…14630674243935600639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.248 × 10⁹⁹(100-digit number)

22486346278172896175…29261348487871201279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.497 × 10⁹⁹(100-digit number)

44972692556345792351…58522696975742402559

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 #1,512,743

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