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Block #519,210

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2014, 2:24:56 AM Β· Difficulty 10.8552 Β· 6,307,175 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ed22def360020ad41ed1eb34ea36c0843d1eff49f5056ed9f986f5d4057225d9
View on Chainz β†—

Height

#519,210

Difficulty

10.855199

Transactions

1

Size

202 B

Version

2

Bits

0adaee58

Nonce

455,042,618

Timestamp

5/1/2014, 2:24:56 AM

Confirmations

6,307,175

Merkle Root

7946255c9eba6b25ac58eb53a7b5e25df4f30a92cf822a3553c5cb725dff8a1e
Transactions (1)
Coinbase7946255c9eba6b…c5cb725dff8a1e
1 in β†’ 1 out8.4700 XPM110 B
AQUVgaeW…EEXgSoMs
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.

3.049 Γ— 10⁹⁸(99-digit number)
30490081532810036572…92361968326453752960
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
3.049 Γ— 10⁹⁸(99-digit number)
30490081532810036572…92361968326453752961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.098 Γ— 10⁹⁸(99-digit number)
60980163065620073144…84723936652907505921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.219 Γ— 10⁹⁹(100-digit number)
12196032613124014628…69447873305815011841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.439 Γ— 10⁹⁹(100-digit number)
24392065226248029257…38895746611630023681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.878 Γ— 10⁹⁹(100-digit number)
48784130452496058515…77791493223260047361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.756 Γ— 10⁹⁹(100-digit number)
97568260904992117031…55582986446520094721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.951 Γ— 10¹⁰⁰(101-digit number)
19513652180998423406…11165972893040189441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.902 Γ— 10¹⁰⁰(101-digit number)
39027304361996846812…22331945786080378881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.805 Γ— 10¹⁰⁰(101-digit number)
78054608723993693625…44663891572160757761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.561 Γ— 10¹⁰¹(102-digit number)
15610921744798738725…89327783144321515521
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 519210

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 ed22def360020ad41ed1eb34ea36c0843d1eff49f5056ed9f986f5d4057225d9

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 #519,210 on Chainz β†—
Circulating Supply:57,855,217 XPMΒ·at block #6,826,384 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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