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Home/Chain Registry/Block #2,833,201

Block #2,833,201

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2018, 2:20:05 PM Β· Difficulty 11.7149 Β· 4,009,691 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
821cb73ad915f4e2ec3b2446af6363b5cab4301fe91b2788de7d3bf98c93f521
View on Chainz β†—

Difficulty

11.714883

Transactions

1

Size

200 B

Version

2

Bits

0bb70291

Nonce

1,042,567,891

Timestamp

9/10/2018, 2:20:05 PM

Confirmations

4,009,691

Merkle Root

fc41a2646e2e5da5ad2014ad693fcb0c83afaa5069bef31dc92fb41ca63ea36c
Transactions (1)
Coinbasefc41a2646e2e5d…2fb41ca63ea36c
1 in β†’ 1 out7.2700 XPM110 B
Adhi2JcH…diaP14C2
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.

7.695 Γ— 10⁹⁴(95-digit number)
76959143142137918515…93689990994834122080
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
7.695 Γ— 10⁹⁴(95-digit number)
76959143142137918515…93689990994834122081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.539 Γ— 10⁹⁡(96-digit number)
15391828628427583703…87379981989668244161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.078 Γ— 10⁹⁡(96-digit number)
30783657256855167406…74759963979336488321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.156 Γ— 10⁹⁡(96-digit number)
61567314513710334812…49519927958672976641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.231 Γ— 10⁹⁢(97-digit number)
12313462902742066962…99039855917345953281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.462 Γ— 10⁹⁢(97-digit number)
24626925805484133924…98079711834691906561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.925 Γ— 10⁹⁢(97-digit number)
49253851610968267849…96159423669383813121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.850 Γ— 10⁹⁢(97-digit number)
98507703221936535699…92318847338767626241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.970 Γ— 10⁹⁷(98-digit number)
19701540644387307139…84637694677535252481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.940 Γ— 10⁹⁷(98-digit number)
39403081288774614279…69275389355070504961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.880 Γ— 10⁹⁷(98-digit number)
78806162577549228559…38550778710141009921
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2833201

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 821cb73ad915f4e2ec3b2446af6363b5cab4301fe91b2788de7d3bf98c93f521

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 #2,833,201 on Chainz β†—
Circulating Supply:57,987,483 XPMΒ·at block #6,842,891 Β· updates every 60s
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