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Block #518,168

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2014, 10:26:31 AM Β· Difficulty 10.8528 Β· 6,308,137 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
95ee9efd5fd3b23f858aba9355cfc7519610ce30aa56b17f2e7e12ed2514a044
View on Chainz β†—

Height

#518,168

Difficulty

10.852755

Transactions

1

Size

208 B

Version

2

Bits

0ada4e2c

Nonce

114,809,519

Timestamp

4/30/2014, 10:26:31 AM

Confirmations

6,308,137

Merkle Root

b367571b639e1218923a005fa359cac9ef11c5ec79e4f59d4a1ef90ad0984f32
Transactions (1)
Coinbaseb367571b639e12…1ef90ad0984f32
1 in β†’ 1 out8.4800 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.

2.547 Γ— 10⁹⁸(99-digit number)
25476596658944364033…12291883721307006000
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
2.547 Γ— 10⁹⁸(99-digit number)
25476596658944364033…12291883721307006001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.095 Γ— 10⁹⁸(99-digit number)
50953193317888728066…24583767442614012001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.019 Γ— 10⁹⁹(100-digit number)
10190638663577745613…49167534885228024001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.038 Γ— 10⁹⁹(100-digit number)
20381277327155491226…98335069770456048001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.076 Γ— 10⁹⁹(100-digit number)
40762554654310982452…96670139540912096001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.152 Γ— 10⁹⁹(100-digit number)
81525109308621964905…93340279081824192001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.630 Γ— 10¹⁰⁰(101-digit number)
16305021861724392981…86680558163648384001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.261 Γ— 10¹⁰⁰(101-digit number)
32610043723448785962…73361116327296768001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.522 Γ— 10¹⁰⁰(101-digit number)
65220087446897571924…46722232654593536001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.304 Γ— 10¹⁰¹(102-digit number)
13044017489379514384…93444465309187072001
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 518168

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 95ee9efd5fd3b23f858aba9355cfc7519610ce30aa56b17f2e7e12ed2514a044

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 #518,168 on Chainz β†—
Circulating Supply:57,854,579 XPMΒ·at block #6,826,304 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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