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Home/Chain Registry/Block #2,843,254

Block #2,843,254

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/17/2018, 10:35:33 AM Β· Difficulty 11.7261 Β· 3,995,866 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
60d919754e4976dfdaecf8f4a539ec412a87012e1f17455c444c49e02ca1144d
View on Chainz β†—

Difficulty

11.726120

Transactions

1

Size

201 B

Version

2

Bits

0bb9e302

Nonce

259,463,303

Timestamp

9/17/2018, 10:35:33 AM

Confirmations

3,995,866

Merkle Root

88c5dbd68d298ab8dd969d919686e5ea825a2ccd03a6c88588cdc7157f45844d
Transactions (1)
Coinbase88c5dbd68d298a…cdc7157f45844d
1 in β†’ 1 out7.2600 XPM110 B
AGomvxzc…ZaHLXuJB
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.

1.445 Γ— 10⁹⁢(97-digit number)
14455361435590002233…27362630855860320000
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
1.445 Γ— 10⁹⁢(97-digit number)
14455361435590002233…27362630855860319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.891 Γ— 10⁹⁢(97-digit number)
28910722871180004466…54725261711720639999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.782 Γ— 10⁹⁢(97-digit number)
57821445742360008933…09450523423441279999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.156 Γ— 10⁹⁷(98-digit number)
11564289148472001786…18901046846882559999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.312 Γ— 10⁹⁷(98-digit number)
23128578296944003573…37802093693765119999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.625 Γ— 10⁹⁷(98-digit number)
46257156593888007146…75604187387530239999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.251 Γ— 10⁹⁷(98-digit number)
92514313187776014293…51208374775060479999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.850 Γ— 10⁹⁸(99-digit number)
18502862637555202858…02416749550120959999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.700 Γ— 10⁹⁸(99-digit number)
37005725275110405717…04833499100241919999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.401 Γ— 10⁹⁸(99-digit number)
74011450550220811434…09666998200483839999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.480 Γ— 10⁹⁹(100-digit number)
14802290110044162286…19333996400967679999
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 2843254

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 60d919754e4976dfdaecf8f4a539ec412a87012e1f17455c444c49e02ca1144d

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 #2,843,254 on Chainz β†—
Circulating Supply:57,957,235 XPMΒ·at block #6,839,119 Β· updates every 60s
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