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Block #2,641,483

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 9:05:42 AM Β· Difficulty 11.6217 Β· 4,190,698 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
54727260f2d2a7c58103abd0e0eac86a52f3eed4a17ea53ef69c0e4daf59a5d9
View on Chainz β†—

Difficulty

11.621654

Transactions

1

Size

200 B

Version

2

Bits

0b9f24be

Nonce

757,606,951

Timestamp

5/1/2018, 9:05:42 AM

Confirmations

4,190,698

Merkle Root

a2a591526ed52aa3ed4b123b3ad8535eed6fd09ec0173605be92ee13612a4772
Transactions (1)
Coinbasea2a591526ed52a…92ee13612a4772
1 in β†’ 1 out7.3900 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.

2.931 Γ— 10⁹⁡(96-digit number)
29313488337641429355…64750943482349473120
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
2.931 Γ— 10⁹⁡(96-digit number)
29313488337641429355…64750943482349473121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.862 Γ— 10⁹⁡(96-digit number)
58626976675282858711…29501886964698946241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.172 Γ— 10⁹⁢(97-digit number)
11725395335056571742…59003773929397892481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.345 Γ— 10⁹⁢(97-digit number)
23450790670113143484…18007547858795784961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.690 Γ— 10⁹⁢(97-digit number)
46901581340226286969…36015095717591569921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.380 Γ— 10⁹⁢(97-digit number)
93803162680452573938…72030191435183139841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.876 Γ— 10⁹⁷(98-digit number)
18760632536090514787…44060382870366279681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.752 Γ— 10⁹⁷(98-digit number)
37521265072181029575…88120765740732559361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.504 Γ— 10⁹⁷(98-digit number)
75042530144362059151…76241531481465118721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.500 Γ— 10⁹⁸(99-digit number)
15008506028872411830…52483062962930237441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.001 Γ— 10⁹⁸(99-digit number)
30017012057744823660…04966125925860474881
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 2641483

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 54727260f2d2a7c58103abd0e0eac86a52f3eed4a17ea53ef69c0e4daf59a5d9

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 #2,641,483 on Chainz β†—
Circulating Supply:57,901,583 XPMΒ·at block #6,832,180 Β· updates every 60s
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