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Block #411,467

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/19/2014, 7:03:38 PM Β· Difficulty 10.4285 Β· 6,387,357 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dd03a44b763578ba979adc09fe05af973201442bf14976391ef9958a8a5a48fa
View on Chainz β†—

Height

#411,467

Difficulty

10.428523

Transactions

1

Size

192 B

Version

2

Bits

0a6db3ac

Nonce

36,138

Timestamp

2/19/2014, 7:03:38 PM

Confirmations

6,387,357

Merkle Root

b9c315eb12b7f7147a9de1ed912b70dbce675a29ba1c01b280b0fd3c7405f6c1
Transactions (1)
Coinbaseb9c315eb12b7f7…b0fd3c7405f6c1
1 in β†’ 1 out9.1800 XPM100 B
AaXb6Ldz…XefG91jF
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.

7.949 Γ— 10⁹⁹(100-digit number)
79490121829091744898…23635626174483110400
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
7.949 Γ— 10⁹⁹(100-digit number)
79490121829091744898…23635626174483110399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.589 Γ— 10¹⁰⁰(101-digit number)
15898024365818348979…47271252348966220799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.179 Γ— 10¹⁰⁰(101-digit number)
31796048731636697959…94542504697932441599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.359 Γ— 10¹⁰⁰(101-digit number)
63592097463273395919…89085009395864883199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.271 Γ— 10¹⁰¹(102-digit number)
12718419492654679183…78170018791729766399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.543 Γ— 10¹⁰¹(102-digit number)
25436838985309358367…56340037583459532799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.087 Γ— 10¹⁰¹(102-digit number)
50873677970618716735…12680075166919065599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.017 Γ— 10¹⁰²(103-digit number)
10174735594123743347…25360150333838131199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.034 Γ— 10¹⁰²(103-digit number)
20349471188247486694…50720300667676262399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.069 Γ— 10¹⁰²(103-digit number)
40698942376494973388…01440601335352524799
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 411467

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 dd03a44b763578ba979adc09fe05af973201442bf14976391ef9958a8a5a48fa

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 #411,467 on Chainz β†—
Circulating Supply:57,634,621 XPMΒ·at block #6,798,823 Β· updates every 60s
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