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Home/Chain Registry/Block #2,818,007

Block #2,818,007

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/31/2018, 6:15:39 AM Β· Difficulty 11.6962 Β· 4,024,982 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7af296f6e38f78da0d7af4a10243b03e52a0f17e164b19e8cd4e2e85ad2b73a8
View on Chainz β†—

Difficulty

11.696217

Transactions

1

Size

200 B

Version

2

Bits

0bb23b4f

Nonce

75,866,059

Timestamp

8/31/2018, 6:15:39 AM

Confirmations

4,024,982

Merkle Root

a75154d728ea4d70041750a4a6a897eb6b43c961b56bf1ca4a9fb42daead0693
Transactions (1)
Coinbasea75154d728ea4d…9fb42daead0693
1 in β†’ 1 out7.3000 XPM110 B
AafG8LVF…HNin7xv2
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.

7.012 Γ— 10⁹⁡(96-digit number)
70126877851025406098…71466230712213190960
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
7.012 Γ— 10⁹⁡(96-digit number)
70126877851025406098…71466230712213190959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.402 Γ— 10⁹⁢(97-digit number)
14025375570205081219…42932461424426381919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.805 Γ— 10⁹⁢(97-digit number)
28050751140410162439…85864922848852763839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.610 Γ— 10⁹⁢(97-digit number)
56101502280820324878…71729845697705527679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.122 Γ— 10⁹⁷(98-digit number)
11220300456164064975…43459691395411055359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.244 Γ— 10⁹⁷(98-digit number)
22440600912328129951…86919382790822110719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.488 Γ— 10⁹⁷(98-digit number)
44881201824656259903…73838765581644221439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.976 Γ— 10⁹⁷(98-digit number)
89762403649312519806…47677531163288442879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.795 Γ— 10⁹⁸(99-digit number)
17952480729862503961…95355062326576885759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.590 Γ— 10⁹⁸(99-digit number)
35904961459725007922…90710124653153771519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.180 Γ— 10⁹⁸(99-digit number)
71809922919450015844…81420249306307543039
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 2818007

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 7af296f6e38f78da0d7af4a10243b03e52a0f17e164b19e8cd4e2e85ad2b73a8

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 #2,818,007 on Chainz β†—
Circulating Supply:57,988,268 XPMΒ·at block #6,842,988 Β· updates every 60s
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