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Home/Chain Registry/Block #330,981

Block #330,981

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/27/2013, 1:24:47 AM Β· Difficulty 10.1685 Β· 6,470,061 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f9d9e1458e92b326aea606eeb9c5da24ebb64f46f611bd95e287564def5d73fd
View on Chainz β†—

Height

#330,981

Difficulty

10.168454

Transactions

1

Size

190 B

Version

2

Bits

0a2b1fcf

Nonce

29,692

Timestamp

12/27/2013, 1:24:47 AM

Confirmations

6,470,061

Merkle Root

7fdac7f1b386934b80549c766239e326b78826b3da8c859a05d07e0cbc59c8b8
Transactions (1)
Coinbase7fdac7f1b38693…d07e0cbc59c8b8
1 in β†’ 1 out9.6600 XPM97 B
AbMAHMS8…MwEzMSoj
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.

9.165 Γ— 10¹⁰⁰(101-digit number)
91656193252805309480…78085754788901632000
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
9.165 Γ— 10¹⁰⁰(101-digit number)
91656193252805309480…78085754788901632001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.833 Γ— 10¹⁰¹(102-digit number)
18331238650561061896…56171509577803264001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.666 Γ— 10¹⁰¹(102-digit number)
36662477301122123792…12343019155606528001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.332 Γ— 10¹⁰¹(102-digit number)
73324954602244247584…24686038311213056001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.466 Γ— 10¹⁰²(103-digit number)
14664990920448849516…49372076622426112001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.932 Γ— 10¹⁰²(103-digit number)
29329981840897699033…98744153244852224001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.865 Γ— 10¹⁰²(103-digit number)
58659963681795398067…97488306489704448001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.173 Γ— 10¹⁰³(104-digit number)
11731992736359079613…94976612979408896001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.346 Γ— 10¹⁰³(104-digit number)
23463985472718159226…89953225958817792001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.692 Γ— 10¹⁰³(104-digit number)
46927970945436318453…79906451917635584001
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 330981

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 f9d9e1458e92b326aea606eeb9c5da24ebb64f46f611bd95e287564def5d73fd

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 #330,981 on Chainz β†—
Circulating Supply:57,652,402 XPMΒ·at block #6,801,041 Β· updates every 60s
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