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Home/Chain Registry/Block #2,873,384

Block #2,873,384

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/9/2018, 2:13:37 AM Β· Difficulty 11.6640 Β· 3,969,715 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ed382d58f49e5ca17481fedd015364b42a64461474bd9b1382ab9cdbeb6a257
View on Chainz β†—

Difficulty

11.663994

Transactions

1

Size

201 B

Version

2

Bits

0ba9fb8a

Nonce

454,938,205

Timestamp

10/9/2018, 2:13:37 AM

Confirmations

3,969,715

Merkle Root

0972caff1fc5ff1082b00753a187334f5bc7964420b78e100c2edfa0623bbd99
Transactions (1)
Coinbase0972caff1fc5ff…2edfa0623bbd99
1 in β†’ 1 out7.3400 XPM110 B
AUZ8LLD4…svNauSmf
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.

3.125 Γ— 10⁹⁷(98-digit number)
31250441189534352104…88664349187952476160
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
3.125 Γ— 10⁹⁷(98-digit number)
31250441189534352104…88664349187952476161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.250 Γ— 10⁹⁷(98-digit number)
62500882379068704208…77328698375904952321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.250 Γ— 10⁹⁸(99-digit number)
12500176475813740841…54657396751809904641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.500 Γ— 10⁹⁸(99-digit number)
25000352951627481683…09314793503619809281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.000 Γ— 10⁹⁸(99-digit number)
50000705903254963366…18629587007239618561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.000 Γ— 10⁹⁹(100-digit number)
10000141180650992673…37259174014479237121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.000 Γ— 10⁹⁹(100-digit number)
20000282361301985346…74518348028958474241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.000 Γ— 10⁹⁹(100-digit number)
40000564722603970693…49036696057916948481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.000 Γ— 10⁹⁹(100-digit number)
80001129445207941386…98073392115833896961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.600 Γ— 10¹⁰⁰(101-digit number)
16000225889041588277…96146784231667793921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.200 Γ— 10¹⁰⁰(101-digit number)
32000451778083176554…92293568463335587841
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2873384

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 6ed382d58f49e5ca17481fedd015364b42a64461474bd9b1382ab9cdbeb6a257

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 #2,873,384 on Chainz β†—
Circulating Supply:57,989,155 XPMΒ·at block #6,843,098 Β· updates every 60s
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