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Home/Chain Registry/Block #2,084,321

Block #2,084,321

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/23/2017, 1:33:20 PM Β· Difficulty 10.8726 Β· 4,746,819 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c4168c7cccef378fd895afd3fef390c658ff56f92378f95ca879b5762b58d29d
View on Chainz β†—

Difficulty

10.872606

Transactions

1

Size

201 B

Version

2

Bits

0adf631f

Nonce

688,929,694

Timestamp

4/23/2017, 1:33:20 PM

Confirmations

4,746,819

Merkle Root

4014c108c816dd16c360170e6ccb4f1736a64714a272bc3ad3185d93f4624aa1
Transactions (1)
Coinbase4014c108c816dd…185d93f4624aa1
1 in β†’ 1 out8.4500 XPM110 B
AXGnaJzV…XZY5nQn6
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.

7.943 Γ— 10⁹⁢(97-digit number)
79437532280957891669…26637758231276144640
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
7.943 Γ— 10⁹⁢(97-digit number)
79437532280957891669…26637758231276144641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.588 Γ— 10⁹⁷(98-digit number)
15887506456191578333…53275516462552289281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.177 Γ— 10⁹⁷(98-digit number)
31775012912383156667…06551032925104578561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.355 Γ— 10⁹⁷(98-digit number)
63550025824766313335…13102065850209157121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.271 Γ— 10⁹⁸(99-digit number)
12710005164953262667…26204131700418314241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.542 Γ— 10⁹⁸(99-digit number)
25420010329906525334…52408263400836628481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.084 Γ— 10⁹⁸(99-digit number)
50840020659813050668…04816526801673256961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.016 Γ— 10⁹⁹(100-digit number)
10168004131962610133…09633053603346513921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.033 Γ— 10⁹⁹(100-digit number)
20336008263925220267…19266107206693027841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.067 Γ— 10⁹⁹(100-digit number)
40672016527850440534…38532214413386055681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.134 Γ— 10⁹⁹(100-digit number)
81344033055700881069…77064428826772111361
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 2084321

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 c4168c7cccef378fd895afd3fef390c658ff56f92378f95ca879b5762b58d29d

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 #2,084,321 on Chainz β†—
Circulating Supply:57,893,267 XPMΒ·at block #6,831,139 Β· updates every 60s
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