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Home/Chain Registry/Block #2,821,556

Block #2,821,556

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/2/2018, 3:33:37 PM Β· Difficulty 11.7030 Β· 4,021,827 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9bb27ee279a598f10e3f65a069a6426bba7189e99623d18c0c8ec46fd5b588df
View on Chainz β†—

Difficulty

11.703042

Transactions

1

Size

200 B

Version

2

Bits

0bb3fa8b

Nonce

1,364,913,416

Timestamp

9/2/2018, 3:33:37 PM

Confirmations

4,021,827

Merkle Root

a2947d31a9661eb8c3f7fbcf400aa32fefbab7b0ffdafdff768f718e63a595eb
Transactions (1)
Coinbasea2947d31a9661e…8f718e63a595eb
1 in β†’ 1 out7.2900 XPM110 B
ATtwCBAJ…neaKgJ8j
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.

2.917 Γ— 10⁹⁴(95-digit number)
29173104368483986140…49523247780753050980
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
2.917 Γ— 10⁹⁴(95-digit number)
29173104368483986140…49523247780753050979
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.834 Γ— 10⁹⁴(95-digit number)
58346208736967972280…99046495561506101959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.166 Γ— 10⁹⁡(96-digit number)
11669241747393594456…98092991123012203919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.333 Γ— 10⁹⁡(96-digit number)
23338483494787188912…96185982246024407839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.667 Γ— 10⁹⁡(96-digit number)
46676966989574377824…92371964492048815679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.335 Γ— 10⁹⁡(96-digit number)
93353933979148755648…84743928984097631359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.867 Γ— 10⁹⁢(97-digit number)
18670786795829751129…69487857968195262719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.734 Γ— 10⁹⁢(97-digit number)
37341573591659502259…38975715936390525439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.468 Γ— 10⁹⁢(97-digit number)
74683147183319004518…77951431872781050879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.493 Γ— 10⁹⁷(98-digit number)
14936629436663800903…55902863745562101759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.987 Γ— 10⁹⁷(98-digit number)
29873258873327601807…11805727491124203519
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 2821556

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 9bb27ee279a598f10e3f65a069a6426bba7189e99623d18c0c8ec46fd5b588df

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 #2,821,556 on Chainz β†—
Circulating Supply:57,991,429 XPMΒ·at block #6,843,382 Β· updates every 60s
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