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Home/Chain Registry/Block #2,634,782

Block #2,634,782

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 12:39:54 AM Β· Difficulty 11.2694 Β· 4,203,289 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
673f000acf31bc36134c44b6e5113fb05a3893ee832da618239261ca5ca1b3f4
View on Chainz β†—

Difficulty

11.269373

Transactions

2

Size

1.32 KB

Version

2

Bits

0b44f5a5

Nonce

337,446,435

Timestamp

4/29/2018, 12:39:54 AM

Confirmations

4,203,289

Merkle Root

322c5ebd9a9f8f1e70943121ea81c7617d532682af8253e467062d297c750e87
Transactions (2)
Coinbase1b3523dfdfd512…547e91216ebf4e
1 in β†’ 1 out7.8800 XPM109 B
Adqah8zh…1WwoHJ9t
54a5b204cdebbb…e7b57ef33bba31
7 in β†’ 3 out2514.4306 XPM1.12 KB
AJf2Z1EU…KAqQeH1LAPi8C85f…Lg5MDieiARnVZ5j4…9WZvuKTr
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.

9.770 Γ— 10⁹³(94-digit number)
97708035925260201332…12775258028580490270
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
9.770 Γ— 10⁹³(94-digit number)
97708035925260201332…12775258028580490271
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.954 Γ— 10⁹⁴(95-digit number)
19541607185052040266…25550516057160980541
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.908 Γ— 10⁹⁴(95-digit number)
39083214370104080533…51101032114321961081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.816 Γ— 10⁹⁴(95-digit number)
78166428740208161066…02202064228643922161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.563 Γ— 10⁹⁡(96-digit number)
15633285748041632213…04404128457287844321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.126 Γ— 10⁹⁡(96-digit number)
31266571496083264426…08808256914575688641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.253 Γ— 10⁹⁡(96-digit number)
62533142992166528853…17616513829151377281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.250 Γ— 10⁹⁢(97-digit number)
12506628598433305770…35233027658302754561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.501 Γ— 10⁹⁢(97-digit number)
25013257196866611541…70466055316605509121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.002 Γ— 10⁹⁢(97-digit number)
50026514393733223082…40932110633211018241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.000 Γ— 10⁹⁷(98-digit number)
10005302878746644616…81864221266422036481
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 2634782

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 673f000acf31bc36134c44b6e5113fb05a3893ee832da618239261ca5ca1b3f4

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 #2,634,782 on Chainz β†—
Circulating Supply:57,948,925 XPMΒ·at block #6,838,070 Β· updates every 60s
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