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Home/Chain Registry/Block #2,683,036

Block #2,683,036

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/29/2018, 1:05:59 PM Β· Difficulty 11.6908 Β· 4,160,067 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a396856d13c69976e991f16d810decfe77fd434278dabc3af6903d05541ef3fa
View on Chainz β†—

Difficulty

11.690778

Transactions

1

Size

200 B

Version

2

Bits

0bb0d6cf

Nonce

1,550,615,464

Timestamp

5/29/2018, 1:05:59 PM

Confirmations

4,160,067

Merkle Root

7da6d3eb4c36608b329fc887101180a7e0fc7df6f47ab506567931f32db71a74
Transactions (1)
Coinbase7da6d3eb4c3660…7931f32db71a74
1 in β†’ 1 out7.3000 XPM110 B
AVNpPEGk…9w7w9nxn
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.

4.353 Γ— 10⁹⁡(96-digit number)
43530524451336680704…38441787516697239040
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
4.353 Γ— 10⁹⁡(96-digit number)
43530524451336680704…38441787516697239041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.706 Γ— 10⁹⁡(96-digit number)
87061048902673361409…76883575033394478081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.741 Γ— 10⁹⁢(97-digit number)
17412209780534672281…53767150066788956161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.482 Γ— 10⁹⁢(97-digit number)
34824419561069344563…07534300133577912321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.964 Γ— 10⁹⁢(97-digit number)
69648839122138689127…15068600267155824641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.392 Γ— 10⁹⁷(98-digit number)
13929767824427737825…30137200534311649281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.785 Γ— 10⁹⁷(98-digit number)
27859535648855475650…60274401068623298561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.571 Γ— 10⁹⁷(98-digit number)
55719071297710951301…20548802137246597121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.114 Γ— 10⁹⁸(99-digit number)
11143814259542190260…41097604274493194241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.228 Γ— 10⁹⁸(99-digit number)
22287628519084380520…82195208548986388481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.457 Γ— 10⁹⁸(99-digit number)
44575257038168761041…64390417097972776961
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 2683036

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 a396856d13c69976e991f16d810decfe77fd434278dabc3af6903d05541ef3fa

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 #2,683,036 on Chainz β†—
Circulating Supply:57,989,187 XPMΒ·at block #6,843,102 Β· updates every 60s
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