Block #84,101

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/26/2013, 2:26:28 PM · Difficulty 9.2723 · 6,726,277 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

886fb6cf2d0dfdd07b268e8e81f35c3b831c5f9705f8f1b502040e68a8a52056

View on Chainz ↗

Height

#84,101

Difficulty

9.272335

Transactions

Size

706 B

Version

Bits

0945b7ba

Nonce

57,355

Timestamp

7/26/2013, 2:26:28 PM

Confirmations

6,726,277

Mined by

⛏️ P2SHAVQuXrGbySy14vrb1e2HbNmXrzzY9BXnLZ

Merkle Root

f5053d0808205b38f49ff7e1d073212628c31aab90e2f23e7d26c632e2e6b8b6

Transactions (2)

Coinbase80b3a82e3c3c3e…8d1adb5c50a4fa

1 in → 1 out11.6200 XPM109 B

AVQuXrGb…zY9BXnLZ

b40b7ce8cb2b51…8b255b16971730

4 in → 1 out48.7100 XPM501 B

AKubZ5rY…L6ewHYWc

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.

9.654 × 10¹⁰⁸(109-digit number)

96548868676365874277…68796548139106360959

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

9.654 × 10¹⁰⁸(109-digit number)

96548868676365874277…68796548139106360959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.930 × 10¹⁰⁹(110-digit number)

19309773735273174855…37593096278212721919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.861 × 10¹⁰⁹(110-digit number)

38619547470546349711…75186192556425443839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.723 × 10¹⁰⁹(110-digit number)

77239094941092699422…50372385112850887679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.544 × 10¹¹⁰(111-digit number)

15447818988218539884…00744770225701775359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.089 × 10¹¹⁰(111-digit number)

30895637976437079768…01489540451403550719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.179 × 10¹¹⁰(111-digit number)

61791275952874159537…02979080902807101439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.235 × 10¹¹¹(112-digit number)

12358255190574831907…05958161805614202879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.471 × 10¹¹¹(112-digit number)

24716510381149663815…11916323611228405759

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 #84,101

Cookie Preferences