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Block #428,301

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/3/2014, 11:41:44 PM Β· Difficulty 10.3482 Β· 6,398,847 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0f6250d67b65ba65dd7f07e8db979f331b97981b1457fb39983ed874a302bd0a
View on Chainz β†—

Height

#428,301

Difficulty

10.348150

Transactions

1

Size

200 B

Version

2

Bits

0a59205f

Nonce

53,649

Timestamp

3/3/2014, 11:41:44 PM

Confirmations

6,398,847

Merkle Root

aede58fa3418ec2bdf05fa17da082984d7660c9ab3032444a49596d96adff2a4
Transactions (1)
Coinbaseaede58fa3418ec…9596d96adff2a4
1 in β†’ 1 out9.3200 XPM109 B
Adxtk9RN…XNE1qWhe
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.

4.172 Γ— 10⁹⁷(98-digit number)
41728057831282620537…35398594780695910400
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
4.172 Γ— 10⁹⁷(98-digit number)
41728057831282620537…35398594780695910401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.345 Γ— 10⁹⁷(98-digit number)
83456115662565241074…70797189561391820801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.669 Γ— 10⁹⁸(99-digit number)
16691223132513048214…41594379122783641601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.338 Γ— 10⁹⁸(99-digit number)
33382446265026096429…83188758245567283201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.676 Γ— 10⁹⁸(99-digit number)
66764892530052192859…66377516491134566401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.335 Γ— 10⁹⁹(100-digit number)
13352978506010438571…32755032982269132801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.670 Γ— 10⁹⁹(100-digit number)
26705957012020877143…65510065964538265601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.341 Γ— 10⁹⁹(100-digit number)
53411914024041754287…31020131929076531201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.068 Γ— 10¹⁰⁰(101-digit number)
10682382804808350857…62040263858153062401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.136 Γ— 10¹⁰⁰(101-digit number)
21364765609616701715…24080527716306124801
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 428301

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 0f6250d67b65ba65dd7f07e8db979f331b97981b1457fb39983ed874a302bd0a

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 #428,301 on Chainz β†—
Circulating Supply:57,861,367 XPMΒ·at block #6,827,147 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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