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Home/Chain Registry/Block #2,846,064

Block #2,846,064

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/19/2018, 8:16:37 AM Β· Difficulty 11.7300 Β· 3,996,095 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1949a3abb142cf8975df4d876591e0c16698f90d544276744a1b10c372c5f0f8
View on Chainz β†—

Difficulty

11.730001

Transactions

1

Size

201 B

Version

2

Bits

0bbae159

Nonce

986,483,203

Timestamp

9/19/2018, 8:16:37 AM

Confirmations

3,996,095

Merkle Root

f7c0366cf685a10d7e3cf4f97e298a7681d7fe01d886d354355324a6a04e2b66
Transactions (1)
Coinbasef7c0366cf685a1…5324a6a04e2b66
1 in β†’ 1 out7.2600 XPM110 B
AJWYgC3P…usAmtkmr
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.

4.692 Γ— 10⁹⁢(97-digit number)
46921980703286419894…03993707169352412160
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
4.692 Γ— 10⁹⁢(97-digit number)
46921980703286419894…03993707169352412161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.384 Γ— 10⁹⁢(97-digit number)
93843961406572839789…07987414338704824321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.876 Γ— 10⁹⁷(98-digit number)
18768792281314567957…15974828677409648641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.753 Γ— 10⁹⁷(98-digit number)
37537584562629135915…31949657354819297281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.507 Γ— 10⁹⁷(98-digit number)
75075169125258271831…63899314709638594561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.501 Γ— 10⁹⁸(99-digit number)
15015033825051654366…27798629419277189121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.003 Γ— 10⁹⁸(99-digit number)
30030067650103308732…55597258838554378241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.006 Γ— 10⁹⁸(99-digit number)
60060135300206617465…11194517677108756481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.201 Γ— 10⁹⁹(100-digit number)
12012027060041323493…22389035354217512961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.402 Γ— 10⁹⁹(100-digit number)
24024054120082646986…44778070708435025921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.804 Γ— 10⁹⁹(100-digit number)
48048108240165293972…89556141416870051841
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 2846064

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 1949a3abb142cf8975df4d876591e0c16698f90d544276744a1b10c372c5f0f8

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 #2,846,064 on Chainz β†—
Circulating Supply:57,981,663 XPMΒ·at block #6,842,158 Β· updates every 60s
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