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Home/Chain Registry/Block #1,682,643

Block #1,682,643

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2016, 2:38:20 AM Β· Difficulty 10.7223 Β· 5,150,106 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c59f8093ca46602ea0e24036944e6f56424ce1bcc4104f0c266e77d1e56ad2df
View on Chainz β†—

Difficulty

10.722337

Transactions

1

Size

199 B

Version

2

Bits

0ab8eb1c

Nonce

923,748,349

Timestamp

7/21/2016, 2:38:20 AM

Confirmations

5,150,106

Merkle Root

5c1678cd6138fca25af28ec01103e5ac005e5323150d871052fb585e6f23bb08
Transactions (1)
Coinbase5c1678cd6138fc…fb585e6f23bb08
1 in β†’ 1 out8.6800 XPM109 B
ANjDvtRH…xFgceHW8
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.

7.110 Γ— 10⁹⁴(95-digit number)
71107586394724642085…33603193966597049600
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
7.110 Γ— 10⁹⁴(95-digit number)
71107586394724642085…33603193966597049599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.422 Γ— 10⁹⁡(96-digit number)
14221517278944928417…67206387933194099199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.844 Γ— 10⁹⁡(96-digit number)
28443034557889856834…34412775866388198399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.688 Γ— 10⁹⁡(96-digit number)
56886069115779713668…68825551732776396799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.137 Γ— 10⁹⁢(97-digit number)
11377213823155942733…37651103465552793599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.275 Γ— 10⁹⁢(97-digit number)
22754427646311885467…75302206931105587199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.550 Γ— 10⁹⁢(97-digit number)
45508855292623770934…50604413862211174399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.101 Γ— 10⁹⁢(97-digit number)
91017710585247541868…01208827724422348799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.820 Γ— 10⁹⁷(98-digit number)
18203542117049508373…02417655448844697599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.640 Γ— 10⁹⁷(98-digit number)
36407084234099016747…04835310897689395199
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 1682643

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 c59f8093ca46602ea0e24036944e6f56424ce1bcc4104f0c266e77d1e56ad2df

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 #1,682,643 on Chainz β†—
Circulating Supply:57,906,153 XPMΒ·at block #6,832,748 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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