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Home/Chain Registry/Block #2,832,013

Block #2,832,013

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2018, 5:23:47 PM Β· Difficulty 11.7187 Β· 4,013,637 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0384627e38e6475b0e21107e0db02146a1d6408fed47209e50706d1aa258f740
View on Chainz β†—

Difficulty

11.718671

Transactions

1

Size

201 B

Version

2

Bits

0bb7facf

Nonce

136,215,201

Timestamp

9/9/2018, 5:23:47 PM

Confirmations

4,013,637

Merkle Root

a652bec8b5e4d0f235628161710a263841ff851cc924afa9ca56fdb3219a584d
Transactions (1)
Coinbasea652bec8b5e4d0…56fdb3219a584d
1 in β†’ 1 out7.2700 XPM110 B
Adtw5pDx…KPHXE8BH
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.

1.009 Γ— 10⁹⁷(98-digit number)
10098431350346356925…30784999059325204480
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
1.009 Γ— 10⁹⁷(98-digit number)
10098431350346356925…30784999059325204481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.019 Γ— 10⁹⁷(98-digit number)
20196862700692713850…61569998118650408961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.039 Γ— 10⁹⁷(98-digit number)
40393725401385427700…23139996237300817921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.078 Γ— 10⁹⁷(98-digit number)
80787450802770855401…46279992474601635841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.615 Γ— 10⁹⁸(99-digit number)
16157490160554171080…92559984949203271681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.231 Γ— 10⁹⁸(99-digit number)
32314980321108342160…85119969898406543361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.462 Γ— 10⁹⁸(99-digit number)
64629960642216684321…70239939796813086721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.292 Γ— 10⁹⁹(100-digit number)
12925992128443336864…40479879593626173441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.585 Γ— 10⁹⁹(100-digit number)
25851984256886673728…80959759187252346881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.170 Γ— 10⁹⁹(100-digit number)
51703968513773347457…61919518374504693761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.034 Γ— 10¹⁰⁰(101-digit number)
10340793702754669491…23839036749009387521
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 2832013

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 0384627e38e6475b0e21107e0db02146a1d6408fed47209e50706d1aa258f740

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 #2,832,013 on Chainz β†—
Circulating Supply:58,009,649 XPMΒ·at block #6,845,649 Β· updates every 60s
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