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Home/Chain Registry/Block #2,811,563

Block #2,811,563

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/27/2018, 2:15:20 AM Β· Difficulty 11.6680 Β· 4,032,864 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6f4eef5c870a97b29805274f7313ba94f91ef8cd4a1136c042a3ef59afc41e81
View on Chainz β†—

Difficulty

11.668034

Transactions

1

Size

200 B

Version

2

Bits

0bab0447

Nonce

190,254,795

Timestamp

8/27/2018, 2:15:20 AM

Confirmations

4,032,864

Merkle Root

56fc279c74df10fb123dd7efb751ace715cfdc692073b53a6c66a8d7e25973d0
Transactions (1)
Coinbase56fc279c74df10…66a8d7e25973d0
1 in β†’ 1 out7.3300 XPM110 B
ATjv2ZQH…6Rxa1o4b
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.

8.568 Γ— 10⁹⁴(95-digit number)
85689285185405300024…93810717486504096620
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
8.568 Γ— 10⁹⁴(95-digit number)
85689285185405300024…93810717486504096619
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.713 Γ— 10⁹⁡(96-digit number)
17137857037081060004…87621434973008193239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.427 Γ— 10⁹⁡(96-digit number)
34275714074162120009…75242869946016386479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.855 Γ— 10⁹⁡(96-digit number)
68551428148324240019…50485739892032772959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.371 Γ— 10⁹⁢(97-digit number)
13710285629664848003…00971479784065545919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.742 Γ— 10⁹⁢(97-digit number)
27420571259329696007…01942959568131091839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.484 Γ— 10⁹⁢(97-digit number)
54841142518659392015…03885919136262183679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.096 Γ— 10⁹⁷(98-digit number)
10968228503731878403…07771838272524367359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.193 Γ— 10⁹⁷(98-digit number)
21936457007463756806…15543676545048734719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.387 Γ— 10⁹⁷(98-digit number)
43872914014927513612…31087353090097469439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.774 Γ— 10⁹⁷(98-digit number)
87745828029855027225…62174706180194938879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2811563

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 6f4eef5c870a97b29805274f7313ba94f91ef8cd4a1136c042a3ef59afc41e81

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 #2,811,563 on Chainz β†—
Circulating Supply:57,999,812 XPMΒ·at block #6,844,426 Β· updates every 60s
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