Home/Chain Registry/Block #318,590

Block #318,590

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/18/2013, 11:21:38 AM · Difficulty 10.1607 · 6,498,728 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

937fe222406c56a8baff100b759ea73f8550b7b57e83814706bf8af00a4c929e

View on Chainz ↗

Height

#318,590

Difficulty

10.160734

Transactions

Size

2.43 KB

Version

Bits

0a2925dc

Nonce

90,343

Timestamp

12/18/2013, 11:21:38 AM

Confirmations

6,498,728

Merkle Root

222c74dbc7adbbe0dedf485f1c2452de087a57d569d7042abf02f6677ecc4bff

Transactions (4)

Coinbasef5eb9331c365a3…1843e5f9d8a409

1 in → 28 out9.6500 XPM1015 B

Aac9Hjdg…P4ktypc3 AZemWJAo…6jhDtieG Ad9pSzHt…cpJ3y2zz AKzkYQaQ…zR4FspJZ AMbCuLHZ…WSoStwkc

e63800afde0c44…9d4e287ba130ec

6 in → 1 out17.6920 XPM931 B

AS6wjyQC…E2BfJdMN

673bae5d915da0…cadc0a8931d6c2

1 in → 2 out4.5943 XPM225 B

AJq2Rm1q…9ZSaZH8E AV9kRYW8…m84GjRbG

8509130580fa77…585f9917a6204e

1 in → 2 out4.4920 XPM226 B

AN1negAf…LWnhVvRp AVtFVni1…orGFZJEE

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.

1.550 × 10¹⁰⁵(106-digit number)

15509096667178384081…51907435685574735360

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

1.550 × 10¹⁰⁵(106-digit number)

15509096667178384081…51907435685574735361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.101 × 10¹⁰⁵(106-digit number)

31018193334356768162…03814871371149470721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.203 × 10¹⁰⁵(106-digit number)

62036386668713536325…07629742742298941441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.240 × 10¹⁰⁶(107-digit number)

12407277333742707265…15259485484597882881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.481 × 10¹⁰⁶(107-digit number)

24814554667485414530…30518970969195765761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.962 × 10¹⁰⁶(107-digit number)

49629109334970829060…61037941938391531521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.925 × 10¹⁰⁶(107-digit number)

99258218669941658120…22075883876783063041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.985 × 10¹⁰⁷(108-digit number)

19851643733988331624…44151767753566126081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.970 × 10¹⁰⁷(108-digit number)

39703287467976663248…88303535507132252161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.940 × 10¹⁰⁷(108-digit number)

79406574935953326496…76607071014264504321

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 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.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

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, …

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 318590

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 937fe222406c56a8baff100b759ea73f8550b7b57e83814706bf8af00a4c929e

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #318,590 on Chainz ↗

Block #318,590

Cookie Preferences