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Block #411,468

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/19/2014, 7:06:42 PM Β· Difficulty 10.4286 Β· 6,394,361 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
434fedbcfdced90c7e5aebfe8ba271e01a9786cd4680e394948ef43fc82bb3cb
View on Chainz β†—

Height

#411,468

Difficulty

10.428608

Transactions

1

Size

203 B

Version

2

Bits

0a6db93f

Nonce

546,491

Timestamp

2/19/2014, 7:06:42 PM

Confirmations

6,394,361

Merkle Root

7de90e8fbf51b185cf6e697272868d13047d7ca1878ee5f514935dfd3834b852
Transactions (1)
Coinbase7de90e8fbf51b1…935dfd3834b852
1 in β†’ 1 out9.1800 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.

6.806 Γ— 10¹⁰⁰(101-digit number)
68069243484984976832…46317037063389562880
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
6.806 Γ— 10¹⁰⁰(101-digit number)
68069243484984976832…46317037063389562879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.361 Γ— 10¹⁰¹(102-digit number)
13613848696996995366…92634074126779125759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.722 Γ— 10¹⁰¹(102-digit number)
27227697393993990732…85268148253558251519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.445 Γ— 10¹⁰¹(102-digit number)
54455394787987981465…70536296507116503039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.089 Γ— 10¹⁰²(103-digit number)
10891078957597596293…41072593014233006079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.178 Γ— 10¹⁰²(103-digit number)
21782157915195192586…82145186028466012159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.356 Γ— 10¹⁰²(103-digit number)
43564315830390385172…64290372056932024319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.712 Γ— 10¹⁰²(103-digit number)
87128631660780770344…28580744113864048639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.742 Γ— 10¹⁰³(104-digit number)
17425726332156154068…57161488227728097279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.485 Γ— 10¹⁰³(104-digit number)
34851452664312308137…14322976455456194559
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 411468

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 434fedbcfdced90c7e5aebfe8ba271e01a9786cd4680e394948ef43fc82bb3cb

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 #411,468 on Chainz β†—
Circulating Supply:57,690,719 XPMΒ·at block #6,805,828 Β· updates every 60s
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