Block #84,504

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 7/26/2013, 9:13:39 PM · Difficulty 9.2717 · 6,718,163 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

db91f47bae8ca7e5cf11dac0840c188fe41ddb8fb44fc24fe7e2eff965fed35a

View on Chainz ↗

Height

#84,504

Difficulty

9.271743

Transactions

Size

206 B

Version

Bits

094590f1

Nonce

95,870

Timestamp

7/26/2013, 9:13:39 PM

Confirmations

6,718,163

Mined by

⛏️ P2SHAcBadmkptMo3EwP8cg9ZUyqvJMGmhL921o

Merkle Root

305adcbd35f230b0ffc9fc5970400721dea5ebae4c923534171f1128ce66724c

Transactions (1)

Coinbase305adcbd35f230…1f1128ce66724c

1 in → 1 out11.6200 XPM109 B

AcBadmkp…GmhL921o

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.

1.597 × 10¹¹¹(112-digit number)

15979732940552085061…04298864573513728799

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

1.597 × 10¹¹¹(112-digit number)

15979732940552085061…04298864573513728799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.195 × 10¹¹¹(112-digit number)

31959465881104170122…08597729147027457599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.391 × 10¹¹¹(112-digit number)

63918931762208340244…17195458294054915199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.278 × 10¹¹²(113-digit number)

12783786352441668048…34390916588109830399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.556 × 10¹¹²(113-digit number)

25567572704883336097…68781833176219660799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.113 × 10¹¹²(113-digit number)

51135145409766672195…37563666352439321599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.022 × 10¹¹³(114-digit number)

10227029081953334439…75127332704878643199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.045 × 10¹¹³(114-digit number)

20454058163906668878…50254665409757286399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.090 × 10¹¹³(114-digit number)

40908116327813337756…00509330819514572799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.181 × 10¹¹³(114-digit number)

81816232655626675512…01018661639029145599

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