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Home/Chain Registry/Block #1,823,587

Block #1,823,587

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/25/2016, 1:02:17 PM Β· Difficulty 10.8197 Β· 4,993,419 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
49a14ff771507624aed368e94bb35dcf3a18d18e4619052d0b81abcef9d6e32d
View on Chainz β†—

Difficulty

10.819722

Transactions

1

Size

200 B

Version

2

Bits

0ad1d94b

Nonce

1,485,542,182

Timestamp

10/25/2016, 1:02:17 PM

Confirmations

4,993,419

Merkle Root

56bdbcccb5b7ce9d621086cce2987565852f49a092f516b15ea0f9d41e8bd868
Transactions (1)
Coinbase56bdbcccb5b7ce…a0f9d41e8bd868
1 in β†’ 1 out8.5300 XPM110 B
ATyGhNX6…SWs1YnoD
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.

2.659 Γ— 10⁹⁴(95-digit number)
26592737689447152676…31943550152891648000
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
2.659 Γ— 10⁹⁴(95-digit number)
26592737689447152676…31943550152891647999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.318 Γ— 10⁹⁴(95-digit number)
53185475378894305353…63887100305783295999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.063 Γ— 10⁹⁡(96-digit number)
10637095075778861070…27774200611566591999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.127 Γ— 10⁹⁡(96-digit number)
21274190151557722141…55548401223133183999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.254 Γ— 10⁹⁡(96-digit number)
42548380303115444282…11096802446266367999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.509 Γ— 10⁹⁡(96-digit number)
85096760606230888564…22193604892532735999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.701 Γ— 10⁹⁢(97-digit number)
17019352121246177712…44387209785065471999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.403 Γ— 10⁹⁢(97-digit number)
34038704242492355425…88774419570130943999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.807 Γ— 10⁹⁢(97-digit number)
68077408484984710851…77548839140261887999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.361 Γ— 10⁹⁷(98-digit number)
13615481696996942170…55097678280523775999
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 1823587

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 49a14ff771507624aed368e94bb35dcf3a18d18e4619052d0b81abcef9d6e32d

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 #1,823,587 on Chainz β†—
Circulating Supply:57,780,081 XPMΒ·at block #6,817,005 Β· updates every 60s
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