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Home/Chain Registry/Block #433,664

Block #433,664

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/7/2014, 5:42:49 PM Β· Difficulty 10.3471 Β· 6,392,542 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a06f45afe7cde80a9b5970c8cb4e4f6c20350b1fba917f8f3fb935ada4be8895
View on Chainz β†—

Height

#433,664

Difficulty

10.347109

Transactions

1

Size

201 B

Version

2

Bits

0a58dc28

Nonce

14,664

Timestamp

3/7/2014, 5:42:49 PM

Confirmations

6,392,542

Merkle Root

2f827abadd61b7dd5d93134cbe15e9295a2435f4cb1bd0f29ee959da98005fe9
Transactions (1)
Coinbase2f827abadd61b7…e959da98005fe9
1 in β†’ 1 out9.3300 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.150 Γ— 10⁹⁸(99-digit number)
11504864442261955183…94242927732012281280
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
1.150 Γ— 10⁹⁸(99-digit number)
11504864442261955183…94242927732012281281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.300 Γ— 10⁹⁸(99-digit number)
23009728884523910367…88485855464024562561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.601 Γ— 10⁹⁸(99-digit number)
46019457769047820734…76971710928049125121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.203 Γ— 10⁹⁸(99-digit number)
92038915538095641468…53943421856098250241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.840 Γ— 10⁹⁹(100-digit number)
18407783107619128293…07886843712196500481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.681 Γ— 10⁹⁹(100-digit number)
36815566215238256587…15773687424393000961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.363 Γ— 10⁹⁹(100-digit number)
73631132430476513175…31547374848786001921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.472 Γ— 10¹⁰⁰(101-digit number)
14726226486095302635…63094749697572003841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.945 Γ— 10¹⁰⁰(101-digit number)
29452452972190605270…26189499395144007681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.890 Γ— 10¹⁰⁰(101-digit number)
58904905944381210540…52378998790288015361
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 433664

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 a06f45afe7cde80a9b5970c8cb4e4f6c20350b1fba917f8f3fb935ada4be8895

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 #433,664 on Chainz β†—
Circulating Supply:57,853,778 XPMΒ·at block #6,826,205 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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