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Home/Chain Registry/Block #3,018,759

Block #3,018,759

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/21/2019, 5:50:36 AM Β· Difficulty 11.1711 Β· 3,826,894 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8ad90254dd18ab18dd27367cc89ec36c026ce9e9a0d63927c4c96364a4dca712
View on Chainz β†—

Difficulty

11.171132

Transactions

1

Size

199 B

Version

2

Bits

0b2bcf52

Nonce

1,695,717,871

Timestamp

1/21/2019, 5:50:36 AM

Confirmations

3,826,894

Merkle Root

4d5ec02f9eca5ba48a36774ea14711e083bfdaf4f2a855ece7370ac976b20ac3
Transactions (1)
Coinbase4d5ec02f9eca5b…370ac976b20ac3
1 in β†’ 1 out8.0000 XPM109 B
AUhjokok…k5m93PZR
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.

5.236 Γ— 10⁹⁡(96-digit number)
52362760216482608011…18544715374207239680
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
5.236 Γ— 10⁹⁡(96-digit number)
52362760216482608011…18544715374207239679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.047 Γ— 10⁹⁢(97-digit number)
10472552043296521602…37089430748414479359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.094 Γ— 10⁹⁢(97-digit number)
20945104086593043204…74178861496828958719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.189 Γ— 10⁹⁢(97-digit number)
41890208173186086409…48357722993657917439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.378 Γ— 10⁹⁢(97-digit number)
83780416346372172818…96715445987315834879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.675 Γ— 10⁹⁷(98-digit number)
16756083269274434563…93430891974631669759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.351 Γ— 10⁹⁷(98-digit number)
33512166538548869127…86861783949263339519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.702 Γ— 10⁹⁷(98-digit number)
67024333077097738254…73723567898526679039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.340 Γ— 10⁹⁸(99-digit number)
13404866615419547650…47447135797053358079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.680 Γ— 10⁹⁸(99-digit number)
26809733230839095301…94894271594106716159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.361 Γ— 10⁹⁸(99-digit number)
53619466461678190603…89788543188213432319
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 3018759

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 8ad90254dd18ab18dd27367cc89ec36c026ce9e9a0d63927c4c96364a4dca712

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 #3,018,759 on Chainz β†—
Circulating Supply:58,009,672 XPMΒ·at block #6,845,652 Β· updates every 60s
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