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Home/Chain Registry/Block #2,844,600

Block #2,844,600

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/18/2018, 8:27:57 AM Β· Difficulty 11.7280 Β· 3,994,370 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
19dfd8fc7fef516a31c3f16045bd767cc48d343bf98df5b00e86abd56b412c55
View on Chainz β†—

Difficulty

11.728001

Transactions

1

Size

199 B

Version

2

Bits

0bba5e46

Nonce

281,081,766

Timestamp

9/18/2018, 8:27:57 AM

Confirmations

3,994,370

Merkle Root

290842da17e8b8f528aa72de23f3137f1f094ab427830b46b4048e5d7cdf7b4b
Transactions (1)
Coinbase290842da17e8b8…048e5d7cdf7b4b
1 in β†’ 1 out7.2600 XPM110 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.

3.470 Γ— 10⁹²(93-digit number)
34706731690600903047…56591076715910275760
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
3.470 Γ— 10⁹²(93-digit number)
34706731690600903047…56591076715910275761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.941 Γ— 10⁹²(93-digit number)
69413463381201806095…13182153431820551521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.388 Γ— 10⁹³(94-digit number)
13882692676240361219…26364306863641103041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.776 Γ— 10⁹³(94-digit number)
27765385352480722438…52728613727282206081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.553 Γ— 10⁹³(94-digit number)
55530770704961444876…05457227454564412161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.110 Γ— 10⁹⁴(95-digit number)
11106154140992288975…10914454909128824321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.221 Γ— 10⁹⁴(95-digit number)
22212308281984577950…21828909818257648641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.442 Γ— 10⁹⁴(95-digit number)
44424616563969155901…43657819636515297281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.884 Γ— 10⁹⁴(95-digit number)
88849233127938311802…87315639273030594561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.776 Γ— 10⁹⁡(96-digit number)
17769846625587662360…74631278546061189121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.553 Γ— 10⁹⁡(96-digit number)
35539693251175324720…49262557092122378241
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 2844600

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 19dfd8fc7fef516a31c3f16045bd767cc48d343bf98df5b00e86abd56b412c55

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 #2,844,600 on Chainz β†—
Circulating Supply:57,956,030 XPMΒ·at block #6,838,969 Β· updates every 60s
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