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Home/Chain Registry/Block #411,964

Block #411,964

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/20/2014, 5:11:14 AM Β· Difficulty 10.4167 Β· 6,415,290 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b6b12f035148f338ffa79110cd7749813722d5acf5f287ee53ddd49049a377b0
View on Chainz β†—

Height

#411,964

Difficulty

10.416697

Transactions

1

Size

201 B

Version

2

Bits

0a6aacad

Nonce

50,172

Timestamp

2/20/2014, 5:11:14 AM

Confirmations

6,415,290

Merkle Root

2e596ed31b3f75309abd18ca6c0f3522d35e5fcde7bbcd77115f668b6576de67
Transactions (1)
Coinbase2e596ed31b3f75…5f668b6576de67
1 in β†’ 1 out9.2000 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.

9.174 Γ— 10⁹⁢(97-digit number)
91744057656600571800…11814450436896855040
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
9.174 Γ— 10⁹⁢(97-digit number)
91744057656600571800…11814450436896855039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.834 Γ— 10⁹⁷(98-digit number)
18348811531320114360…23628900873793710079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.669 Γ— 10⁹⁷(98-digit number)
36697623062640228720…47257801747587420159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.339 Γ— 10⁹⁷(98-digit number)
73395246125280457440…94515603495174840319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.467 Γ— 10⁹⁸(99-digit number)
14679049225056091488…89031206990349680639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.935 Γ— 10⁹⁸(99-digit number)
29358098450112182976…78062413980699361279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.871 Γ— 10⁹⁸(99-digit number)
58716196900224365952…56124827961398722559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.174 Γ— 10⁹⁹(100-digit number)
11743239380044873190…12249655922797445119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.348 Γ— 10⁹⁹(100-digit number)
23486478760089746381…24499311845594890239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.697 Γ— 10⁹⁹(100-digit number)
46972957520179492762…48998623691189780479
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 411964

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 b6b12f035148f338ffa79110cd7749813722d5acf5f287ee53ddd49049a377b0

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 #411,964 on Chainz β†—
Circulating Supply:57,862,135 XPMΒ·at block #6,827,253 Β· updates every 60s
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