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Block #364,439

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/18/2014, 1:58:07 AM Β· Difficulty 10.4213 Β· 6,471,932 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d17b3e80c1b5ec6da37afe6d17666c6e930504409aa94f37f530c464e1be1777
View on Chainz β†—

Height

#364,439

Difficulty

10.421251

Transactions

1

Size

202 B

Version

2

Bits

0a6bd720

Nonce

431,628

Timestamp

1/18/2014, 1:58:07 AM

Confirmations

6,471,932

Merkle Root

081c1e753b40de1da06a9ba9a3f11ff4136c134da2ead155cb7201c7544094f0
Transactions (1)
Coinbase081c1e753b40de…7201c7544094f0
1 in β†’ 1 out9.1900 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.

1.048 Γ— 10¹⁰⁰(101-digit number)
10485622899344147039…57244384748059502540
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.048 Γ— 10¹⁰⁰(101-digit number)
10485622899344147039…57244384748059502539
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.097 Γ— 10¹⁰⁰(101-digit number)
20971245798688294078…14488769496119005079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.194 Γ— 10¹⁰⁰(101-digit number)
41942491597376588156…28977538992238010159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.388 Γ— 10¹⁰⁰(101-digit number)
83884983194753176313…57955077984476020319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.677 Γ— 10¹⁰¹(102-digit number)
16776996638950635262…15910155968952040639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.355 Γ— 10¹⁰¹(102-digit number)
33553993277901270525…31820311937904081279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.710 Γ— 10¹⁰¹(102-digit number)
67107986555802541050…63640623875808162559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.342 Γ— 10¹⁰²(103-digit number)
13421597311160508210…27281247751616325119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.684 Γ— 10¹⁰²(103-digit number)
26843194622321016420…54562495503232650239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.368 Γ— 10¹⁰²(103-digit number)
53686389244642032840…09124991006465300479
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 364439

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 d17b3e80c1b5ec6da37afe6d17666c6e930504409aa94f37f530c464e1be1777

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 #364,439 on Chainz β†—
Circulating Supply:57,935,228 XPMΒ·at block #6,836,370 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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