Block #84,983

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/27/2013, 4:10:28 AM · Difficulty 9.2806 · 6,711,146 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d92b75db288eafe606b31483aaf01caa9ee8163deb951dead7e2ad97b047454c

View on Chainz ↗

Height

#84,983

Difficulty

9.280610

Transactions

Size

205 B

Version

Bits

0947d60d

Nonce

8,691

Timestamp

7/27/2013, 4:10:28 AM

Confirmations

6,711,146

Mined by

⛏️ P2SHASXW8s4r1QTq8Djg6zDrh4WCnULM8vqY9U

Merkle Root

a6e8800d59affafbb30a6e3e65ac46618855d46721906fb447ea8482540389e2

Transactions (1)

Coinbasea6e8800d59affa…ea8482540389e2

1 in → 1 out11.5900 XPM109 B

ASXW8s4r…LM8vqY9U

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.

1.661 × 10¹⁰⁹(110-digit number)

16611035711337024377…80651247503834429001

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

1.661 × 10¹⁰⁹(110-digit number)

16611035711337024377…80651247503834429001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.322 × 10¹⁰⁹(110-digit number)

33222071422674048754…61302495007668858001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.644 × 10¹⁰⁹(110-digit number)

66444142845348097508…22604990015337716001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.328 × 10¹¹⁰(111-digit number)

13288828569069619501…45209980030675432001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.657 × 10¹¹⁰(111-digit number)

26577657138139239003…90419960061350864001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.315 × 10¹¹⁰(111-digit number)

53155314276278478006…80839920122701728001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.063 × 10¹¹¹(112-digit number)

10631062855255695601…61679840245403456001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.126 × 10¹¹¹(112-digit number)

21262125710511391202…23359680490806912001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.252 × 10¹¹¹(112-digit number)

42524251421022782405…46719360981613824001

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer