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Block #330,157

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/26/2013, 11:36:23 AM Β· Difficulty 10.1690 Β· 6,471,483 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ffd4f736a8105daf747680f0594be0eea1513cc00716946d81ff202c6449c05d
View on Chainz β†—

Height

#330,157

Difficulty

10.169043

Transactions

1

Size

207 B

Version

2

Bits

0a2b466b

Nonce

145,604

Timestamp

12/26/2013, 11:36:23 AM

Confirmations

6,471,483

Merkle Root

672c29f9efe1d0dc2b34473b28aa68a9ed7f2e61e81533f802330b177a024378
Transactions (1)
Coinbase672c29f9efe1d0…330b177a024378
1 in β†’ 1 out9.6600 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.

2.073 Γ— 10⁹⁷(98-digit number)
20735966584658238497…02809204729229238350
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
2.073 Γ— 10⁹⁷(98-digit number)
20735966584658238497…02809204729229238351
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.147 Γ— 10⁹⁷(98-digit number)
41471933169316476994…05618409458458476701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.294 Γ— 10⁹⁷(98-digit number)
82943866338632953988…11236818916916953401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.658 Γ— 10⁹⁸(99-digit number)
16588773267726590797…22473637833833906801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.317 Γ— 10⁹⁸(99-digit number)
33177546535453181595…44947275667667813601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.635 Γ— 10⁹⁸(99-digit number)
66355093070906363190…89894551335335627201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.327 Γ— 10⁹⁹(100-digit number)
13271018614181272638…79789102670671254401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.654 Γ— 10⁹⁹(100-digit number)
26542037228362545276…59578205341342508801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.308 Γ— 10⁹⁹(100-digit number)
53084074456725090552…19156410682685017601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.061 Γ— 10¹⁰⁰(101-digit number)
10616814891345018110…38312821365370035201
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 330157

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 ffd4f736a8105daf747680f0594be0eea1513cc00716946d81ff202c6449c05d

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 #330,157 on Chainz β†—
Circulating Supply:57,657,200 XPMΒ·at block #6,801,639 Β· updates every 60s
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