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Home/Chain Registry/Block #2,745,194

Block #2,745,194

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/12/2018, 4:44:45 AM Β· Difficulty 11.6470 Β· 4,096,931 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
39ea89574d8ee6c2959b1ae6dafd0e5d0f199bb213511b8dca0f544acfd9ba88
View on Chainz β†—

Difficulty

11.646975

Transactions

1

Size

200 B

Version

2

Bits

0ba5a02a

Nonce

1,958,038,490

Timestamp

7/12/2018, 4:44:45 AM

Confirmations

4,096,931

Merkle Root

980af1691a221f7053a2ae1d6e78e5b2594cc037041d75e95fdc9d91e8a7273e
Transactions (1)
Coinbase980af1691a221f…dc9d91e8a7273e
1 in β†’ 1 out7.3600 XPM109 B
AZtxQr2F…7grUWrUz
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.

2.577 Γ— 10⁹⁢(97-digit number)
25773255005302817947…08652455020001917440
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
2.577 Γ— 10⁹⁢(97-digit number)
25773255005302817947…08652455020001917439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.154 Γ— 10⁹⁢(97-digit number)
51546510010605635894…17304910040003834879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.030 Γ— 10⁹⁷(98-digit number)
10309302002121127178…34609820080007669759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.061 Γ— 10⁹⁷(98-digit number)
20618604004242254357…69219640160015339519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.123 Γ— 10⁹⁷(98-digit number)
41237208008484508715…38439280320030679039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.247 Γ— 10⁹⁷(98-digit number)
82474416016969017431…76878560640061358079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.649 Γ— 10⁹⁸(99-digit number)
16494883203393803486…53757121280122716159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.298 Γ— 10⁹⁸(99-digit number)
32989766406787606972…07514242560245432319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.597 Γ— 10⁹⁸(99-digit number)
65979532813575213945…15028485120490864639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.319 Γ— 10⁹⁹(100-digit number)
13195906562715042789…30056970240981729279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.639 Γ— 10⁹⁹(100-digit number)
26391813125430085578…60113940481963458559
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 2745194

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 39ea89574d8ee6c2959b1ae6dafd0e5d0f199bb213511b8dca0f544acfd9ba88

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 #2,745,194 on Chainz β†—
Circulating Supply:57,981,388 XPMΒ·at block #6,842,124 Β· updates every 60s
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