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Block #522,438

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2014, 1:05:49 AM Β· Difficulty 10.8671 Β· 6,277,815 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
12aa3e4de7e5bc1e3734447544e22bf56e623b23fd65e60c67af7fdb6a0abc86
View on Chainz β†—

Height

#522,438

Difficulty

10.867101

Transactions

1

Size

208 B

Version

2

Bits

0addfa51

Nonce

16,952,836

Timestamp

5/3/2014, 1:05:49 AM

Confirmations

6,277,815

Merkle Root

7580375244fc332a4e2dea9ce18dff4466f8801a778d5eca0515d691761eaf0b
Transactions (1)
Coinbase7580375244fc33…15d691761eaf0b
1 in β†’ 1 out8.4500 XPM116 B
AbwWkWZt…kawDhufa
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.824 Γ— 10⁹⁸(99-digit number)
88249573938032128566…09721003344187235240
Discovered Prime Numbers
p_k = 2^k Γ— 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.

1
origin + 1
8.824 Γ— 10⁹⁸(99-digit number)
88249573938032128566…09721003344187235241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.764 Γ— 10⁹⁹(100-digit number)
17649914787606425713…19442006688374470481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.529 Γ— 10⁹⁹(100-digit number)
35299829575212851426…38884013376748940961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.059 Γ— 10⁹⁹(100-digit number)
70599659150425702853…77768026753497881921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.411 Γ— 10¹⁰⁰(101-digit number)
14119931830085140570…55536053506995763841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.823 Γ— 10¹⁰⁰(101-digit number)
28239863660170281141…11072107013991527681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.647 Γ— 10¹⁰⁰(101-digit number)
56479727320340562282…22144214027983055361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.129 Γ— 10¹⁰¹(102-digit number)
11295945464068112456…44288428055966110721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.259 Γ— 10¹⁰¹(102-digit number)
22591890928136224913…88576856111932221441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.518 Γ— 10¹⁰¹(102-digit number)
45183781856272449826…77153712223864442881
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 522438

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 12aa3e4de7e5bc1e3734447544e22bf56e623b23fd65e60c67af7fdb6a0abc86

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 β†’ Debug Window β†’ 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 #522,438 on Chainz β†—
Circulating Supply:57,646,079 XPMΒ·at block #6,800,252 Β· updates every 60s
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