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Block #492,292

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/15/2014, 12:53:40 AM Β· Difficulty 10.6885 Β· 6,323,500 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c8aff7fc02e822634929d3b314f83253274e42cea4c4ec759a36d83a63e75de2
View on Chainz β†—

Height

#492,292

Difficulty

10.688516

Transactions

1

Size

201 B

Version

2

Bits

0ab0429b

Nonce

40,361,851

Timestamp

4/15/2014, 12:53:40 AM

Confirmations

6,323,500

Merkle Root

b7318582e1f79f6a1a7664d6bbb53c4fe8090803fc3fce0f9632b6f2dbde945c
Transactions (1)
Coinbaseb7318582e1f79f…32b6f2dbde945c
1 in β†’ 1 out8.7400 XPM110 B
Ab1Kd5Pk…vQSyxwRc
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.

2.584 Γ— 10⁹⁷(98-digit number)
25841691659118965656…42966165660827832320
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
2.584 Γ— 10⁹⁷(98-digit number)
25841691659118965656…42966165660827832321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.168 Γ— 10⁹⁷(98-digit number)
51683383318237931312…85932331321655664641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.033 Γ— 10⁹⁸(99-digit number)
10336676663647586262…71864662643311329281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.067 Γ— 10⁹⁸(99-digit number)
20673353327295172525…43729325286622658561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.134 Γ— 10⁹⁸(99-digit number)
41346706654590345050…87458650573245317121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.269 Γ— 10⁹⁸(99-digit number)
82693413309180690100…74917301146490634241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.653 Γ— 10⁹⁹(100-digit number)
16538682661836138020…49834602292981268481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.307 Γ— 10⁹⁹(100-digit number)
33077365323672276040…99669204585962536961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.615 Γ— 10⁹⁹(100-digit number)
66154730647344552080…99338409171925073921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.323 Γ— 10¹⁰⁰(101-digit number)
13230946129468910416…98676818343850147841
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 492292

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 c8aff7fc02e822634929d3b314f83253274e42cea4c4ec759a36d83a63e75de2

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 #492,292 on Chainz β†—
Circulating Supply:57,770,439 XPMΒ·at block #6,815,791 Β· updates every 60s
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