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Home/Chain Registry/Block #2,833,344

Block #2,833,344

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2018, 4:32:24 PM Β· Difficulty 11.7154 Β· 4,011,561 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
73def70c9b6fd899d2a4e120e9f077e3a37abbc8a242b7cbdab8809eec023529
View on Chainz β†—

Difficulty

11.715418

Transactions

1

Size

201 B

Version

2

Bits

0bb725a0

Nonce

62,110,276

Timestamp

9/10/2018, 4:32:24 PM

Confirmations

4,011,561

Merkle Root

8c65c8833f95c59d370641028649aa7b143987640c71cbeb1fa5dab1c441833d
Transactions (1)
Coinbase8c65c8833f95c5…a5dab1c441833d
1 in β†’ 1 out7.2700 XPM110 B
APj62WhD…rvBMnT2o
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.

9.996 Γ— 10⁹⁢(97-digit number)
99966851136646027432…66302928850219878400
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
9.996 Γ— 10⁹⁢(97-digit number)
99966851136646027432…66302928850219878399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.999 Γ— 10⁹⁷(98-digit number)
19993370227329205486…32605857700439756799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.998 Γ— 10⁹⁷(98-digit number)
39986740454658410972…65211715400879513599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.997 Γ— 10⁹⁷(98-digit number)
79973480909316821945…30423430801759027199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.599 Γ— 10⁹⁸(99-digit number)
15994696181863364389…60846861603518054399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.198 Γ— 10⁹⁸(99-digit number)
31989392363726728778…21693723207036108799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.397 Γ— 10⁹⁸(99-digit number)
63978784727453457556…43387446414072217599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.279 Γ— 10⁹⁹(100-digit number)
12795756945490691511…86774892828144435199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.559 Γ— 10⁹⁹(100-digit number)
25591513890981383022…73549785656288870399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.118 Γ— 10⁹⁹(100-digit number)
51183027781962766045…47099571312577740799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.023 Γ— 10¹⁰⁰(101-digit number)
10236605556392553209…94199142625155481599
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 2833344

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 73def70c9b6fd899d2a4e120e9f077e3a37abbc8a242b7cbdab8809eec023529

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 #2,833,344 on Chainz β†—
Circulating Supply:58,003,654 XPMΒ·at block #6,844,904 Β· updates every 60s
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