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Home/Chain Registry/Block #2,822,575

Block #2,822,575

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/3/2018, 8:34:55 AM Β· Difficulty 11.7030 Β· 4,019,258 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9b94b1c6a4cfce0c52ac6f2f67b1cc4e25e1c4f5765717fa820f541149bcdbe7
View on Chainz β†—

Difficulty

11.703004

Transactions

1

Size

201 B

Version

2

Bits

0bb3f80f

Nonce

168,759,192

Timestamp

9/3/2018, 8:34:55 AM

Confirmations

4,019,258

Merkle Root

734221f6c106fee9441dd740b1bd98436f42db1c7c26ff2b2d664d9e6d222a02
Transactions (1)
Coinbase734221f6c106fe…664d9e6d222a02
1 in β†’ 1 out7.2900 XPM110 B
AZtxQr2F…7grUWrUz
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.

8.672 Γ— 10⁹⁢(97-digit number)
86724813243535784403…67384877426795664640
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
8.672 Γ— 10⁹⁢(97-digit number)
86724813243535784403…67384877426795664639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.734 Γ— 10⁹⁷(98-digit number)
17344962648707156880…34769754853591329279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.468 Γ— 10⁹⁷(98-digit number)
34689925297414313761…69539509707182658559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.937 Γ— 10⁹⁷(98-digit number)
69379850594828627522…39079019414365317119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.387 Γ— 10⁹⁸(99-digit number)
13875970118965725504…78158038828730634239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.775 Γ— 10⁹⁸(99-digit number)
27751940237931451008…56316077657461268479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.550 Γ— 10⁹⁸(99-digit number)
55503880475862902017…12632155314922536959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.110 Γ— 10⁹⁹(100-digit number)
11100776095172580403…25264310629845073919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.220 Γ— 10⁹⁹(100-digit number)
22201552190345160807…50528621259690147839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.440 Γ— 10⁹⁹(100-digit number)
44403104380690321614…01057242519380295679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.880 Γ— 10⁹⁹(100-digit number)
88806208761380643228…02114485038760591359
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 2822575

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 9b94b1c6a4cfce0c52ac6f2f67b1cc4e25e1c4f5765717fa820f541149bcdbe7

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 #2,822,575 on Chainz β†—
Circulating Supply:57,979,037 XPMΒ·at block #6,841,832 Β· updates every 60s
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