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Block #439,419

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/11/2014, 4:27:14 PM Β· Difficulty 10.3596 Β· 6,375,600 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fa7f2659d43120ecea24593eff2ea17443d50f6b6c5a33e15fda2e085afcf2ee
View on Chainz β†—

Height

#439,419

Difficulty

10.359598

Transactions

1

Size

201 B

Version

2

Bits

0a5c0ea0

Nonce

152,544

Timestamp

3/11/2014, 4:27:14 PM

Confirmations

6,375,600

Merkle Root

05a0434b80c1181786ddfca22391081d896cd1636fd3bc0055f8fb8315f7049a
Transactions (1)
Coinbase05a0434b80c118…f8fb8315f7049a
1 in β†’ 1 out9.3000 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.

4.901 Γ— 10⁹⁷(98-digit number)
49019291604157639638…87453543577790873600
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
4.901 Γ— 10⁹⁷(98-digit number)
49019291604157639638…87453543577790873599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.803 Γ— 10⁹⁷(98-digit number)
98038583208315279277…74907087155581747199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.960 Γ— 10⁹⁸(99-digit number)
19607716641663055855…49814174311163494399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.921 Γ— 10⁹⁸(99-digit number)
39215433283326111710…99628348622326988799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.843 Γ— 10⁹⁸(99-digit number)
78430866566652223421…99256697244653977599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.568 Γ— 10⁹⁹(100-digit number)
15686173313330444684…98513394489307955199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.137 Γ— 10⁹⁹(100-digit number)
31372346626660889368…97026788978615910399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.274 Γ— 10⁹⁹(100-digit number)
62744693253321778737…94053577957231820799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.254 Γ— 10¹⁰⁰(101-digit number)
12548938650664355747…88107155914463641599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.509 Γ— 10¹⁰⁰(101-digit number)
25097877301328711494…76214311828927283199
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 439419

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 fa7f2659d43120ecea24593eff2ea17443d50f6b6c5a33e15fda2e085afcf2ee

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 #439,419 on Chainz β†—
Circulating Supply:57,764,239 XPMΒ·at block #6,815,018 Β· updates every 60s
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