Block #81,037

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/24/2013, 12:14:05 PM · Difficulty 9.2650 · 6,727,720 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6402c80d55510264cc65575792a00bc4a27a435c50e8a045b06c645bbd27e72d

View on Chainz ↗

Height

#81,037

Difficulty

9.265021

Transactions

Size

730 B

Version

Bits

0943d86a

Nonce

552

Timestamp

7/24/2013, 12:14:05 PM

Confirmations

6,727,720

Mined by

⛏️ P2SHARU96VjERUDexCD5FJZCkvpEvk27xr9LG9

Merkle Root

913d46ddf5e401c5923fbba7a577744fd611dc6df6d1442b179481da3ab3d4f2

Transactions (2)

Coinbase51d20fca93915d…c4649238de6485

1 in → 1 out11.6400 XPM110 B

ARU96VjE…27xr9LG9

d4a0df370aff05…3938d1534665c1

3 in → 2 out399.9753 XPM523 B

AS1wRrUS…Td85AZQe ALqZ91rG…RtQ3C2x3

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.

5.036 × 10¹¹²(113-digit number)

50364505115068710022…47313490250084820189

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

5.036 × 10¹¹²(113-digit number)

50364505115068710022…47313490250084820189

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.007 × 10¹¹³(114-digit number)

10072901023013742004…94626980500169640379

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.014 × 10¹¹³(114-digit number)

20145802046027484008…89253961000339280759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.029 × 10¹¹³(114-digit number)

40291604092054968017…78507922000678561519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.058 × 10¹¹³(114-digit number)

80583208184109936035…57015844001357123039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.611 × 10¹¹⁴(115-digit number)

16116641636821987207…14031688002714246079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.223 × 10¹¹⁴(115-digit number)

32233283273643974414…28063376005428492159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.446 × 10¹¹⁴(115-digit number)

64466566547287948828…56126752010856984319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.289 × 10¹¹⁵(116-digit number)

12893313309457589765…12253504021713968639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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

Block #81,037

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