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Block #2,643,290

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 1:29:46 AM Β· Difficulty 11.6787 Β· 4,190,646 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
538c07c78ca0d7ea778367796b9293fc83bd0362f1489ad04381248330805afc
View on Chainz β†—

Difficulty

11.678707

Transactions

1

Size

200 B

Version

2

Bits

0badbfc1

Nonce

559,410,604

Timestamp

5/2/2018, 1:29:46 AM

Confirmations

4,190,646

Merkle Root

fec5edeeaa7c44438ca04be04d7d6e121c593dbd19880b3d286886980ae74e4d
Transactions (1)
Coinbasefec5edeeaa7c44…6886980ae74e4d
1 in β†’ 1 out7.3200 XPM110 B
AXVhuxkc…DCnEmdrK
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.

1.142 Γ— 10⁹⁡(96-digit number)
11426848015913511031…75216177828633506560
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
1.142 Γ— 10⁹⁡(96-digit number)
11426848015913511031…75216177828633506561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.285 Γ— 10⁹⁡(96-digit number)
22853696031827022062…50432355657267013121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.570 Γ— 10⁹⁡(96-digit number)
45707392063654044124…00864711314534026241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.141 Γ— 10⁹⁡(96-digit number)
91414784127308088248…01729422629068052481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.828 Γ— 10⁹⁢(97-digit number)
18282956825461617649…03458845258136104961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.656 Γ— 10⁹⁢(97-digit number)
36565913650923235299…06917690516272209921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.313 Γ— 10⁹⁢(97-digit number)
73131827301846470599…13835381032544419841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.462 Γ— 10⁹⁷(98-digit number)
14626365460369294119…27670762065088839681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.925 Γ— 10⁹⁷(98-digit number)
29252730920738588239…55341524130177679361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.850 Γ— 10⁹⁷(98-digit number)
58505461841477176479…10683048260355358721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.170 Γ— 10⁹⁸(99-digit number)
11701092368295435295…21366096520710717441
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 2643290

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 538c07c78ca0d7ea778367796b9293fc83bd0362f1489ad04381248330805afc

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 #2,643,290 on Chainz β†—
Circulating Supply:57,915,716 XPMΒ·at block #6,833,935 Β· updates every 60s
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