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Block #2,676,544

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/24/2018, 10:58:35 PM Β· Difficulty 11.6976 Β· 4,159,861 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d6b426d414b865cfa3566f73c7d75aedb0eda4c977a533097e9f1db66b726a22
View on Chainz β†—

Difficulty

11.697569

Transactions

1

Size

200 B

Version

2

Bits

0bb293df

Nonce

53,973,444

Timestamp

5/24/2018, 10:58:35 PM

Confirmations

4,159,861

Merkle Root

2db58430c1e0422f3e31322bc3d756b401626aa0eeb818a8b611ac0a8f810c12
Transactions (1)
Coinbase2db58430c1e042…11ac0a8f810c12
1 in β†’ 1 out7.3000 XPM110 B
Adqah8zh…1WwoHJ9t
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.

4.918 Γ— 10⁹³(94-digit number)
49183549749977319503…50314870918763169870
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
4.918 Γ— 10⁹³(94-digit number)
49183549749977319503…50314870918763169871
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.836 Γ— 10⁹³(94-digit number)
98367099499954639007…00629741837526339741
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.967 Γ— 10⁹⁴(95-digit number)
19673419899990927801…01259483675052679481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.934 Γ— 10⁹⁴(95-digit number)
39346839799981855602…02518967350105358961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.869 Γ— 10⁹⁴(95-digit number)
78693679599963711205…05037934700210717921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.573 Γ— 10⁹⁡(96-digit number)
15738735919992742241…10075869400421435841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.147 Γ— 10⁹⁡(96-digit number)
31477471839985484482…20151738800842871681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.295 Γ— 10⁹⁡(96-digit number)
62954943679970968964…40303477601685743361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.259 Γ— 10⁹⁢(97-digit number)
12590988735994193792…80606955203371486721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.518 Γ— 10⁹⁢(97-digit number)
25181977471988387585…61213910406742973441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.036 Γ— 10⁹⁢(97-digit number)
50363954943976775171…22427820813485946881
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 2676544

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 d6b426d414b865cfa3566f73c7d75aedb0eda4c977a533097e9f1db66b726a22

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 #2,676,544 on Chainz β†—
Circulating Supply:57,935,504 XPMΒ·at block #6,836,404 Β· updates every 60s
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