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Block #430,707

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/5/2014, 4:27:19 PM Β· Difficulty 10.3451 Β· 6,394,837 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
978d8b4f572fab6c1860f8fa2c98a34c0ee8a31dc16b98fb2f117c630b083444
View on Chainz β†—

Height

#430,707

Difficulty

10.345143

Transactions

1

Size

210 B

Version

2

Bits

0a585b49

Nonce

52,038

Timestamp

3/5/2014, 4:27:19 PM

Confirmations

6,394,837

Merkle Root

a36a76a6151fc5b5e8df29eefb3f4bb8924c314c0655b6c3f29004eb01ad5371
Transactions (1)
Coinbasea36a76a6151fc5…9004eb01ad5371
1 in β†’ 1 out9.3300 XPM118 B
APeCKNQa…29psj9Wz
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.

3.023 Γ— 10⁹⁹(100-digit number)
30235011242891730910…82482858411316070400
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
3.023 Γ— 10⁹⁹(100-digit number)
30235011242891730910…82482858411316070401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.047 Γ— 10⁹⁹(100-digit number)
60470022485783461820…64965716822632140801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.209 Γ— 10¹⁰⁰(101-digit number)
12094004497156692364…29931433645264281601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.418 Γ— 10¹⁰⁰(101-digit number)
24188008994313384728…59862867290528563201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.837 Γ— 10¹⁰⁰(101-digit number)
48376017988626769456…19725734581057126401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.675 Γ— 10¹⁰⁰(101-digit number)
96752035977253538912…39451469162114252801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.935 Γ— 10¹⁰¹(102-digit number)
19350407195450707782…78902938324228505601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.870 Γ— 10¹⁰¹(102-digit number)
38700814390901415565…57805876648457011201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.740 Γ— 10¹⁰¹(102-digit number)
77401628781802831130…15611753296914022401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.548 Γ— 10¹⁰²(103-digit number)
15480325756360566226…31223506593828044801
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 430707

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 978d8b4f572fab6c1860f8fa2c98a34c0ee8a31dc16b98fb2f117c630b083444

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 #430,707 on Chainz β†—
Circulating Supply:57,848,451 XPMΒ·at block #6,825,543 Β· updates every 60s
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