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Home/Chain Registry/Block #2,634,621

Block #2,634,621

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/28/2018, 11:22:29 PM Β· Difficulty 11.2570 Β· 4,207,586 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5343387cfe064608ab39207dbb5958832b28df58882c0d55c4292827ac4722d7
View on Chainz β†—

Difficulty

11.257048

Transactions

1

Size

201 B

Version

2

Bits

0b41cde1

Nonce

607,733,212

Timestamp

4/28/2018, 11:22:29 PM

Confirmations

4,207,586

Merkle Root

e875c36ab521ca8a2a3007123c4a6fe971009784aac70d6c6a8777ea45c3ecee
Transactions (1)
Coinbasee875c36ab521ca…8777ea45c3ecee
1 in β†’ 1 out7.8800 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.

4.501 Γ— 10⁹⁢(97-digit number)
45012520623503794057…23039447148041175040
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.501 Γ— 10⁹⁢(97-digit number)
45012520623503794057…23039447148041175039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.002 Γ— 10⁹⁢(97-digit number)
90025041247007588114…46078894296082350079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.800 Γ— 10⁹⁷(98-digit number)
18005008249401517622…92157788592164700159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.601 Γ— 10⁹⁷(98-digit number)
36010016498803035245…84315577184329400319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.202 Γ— 10⁹⁷(98-digit number)
72020032997606070491…68631154368658800639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.440 Γ— 10⁹⁸(99-digit number)
14404006599521214098…37262308737317601279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.880 Γ— 10⁹⁸(99-digit number)
28808013199042428196…74524617474635202559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.761 Γ— 10⁹⁸(99-digit number)
57616026398084856393…49049234949270405119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.152 Γ— 10⁹⁹(100-digit number)
11523205279616971278…98098469898540810239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.304 Γ— 10⁹⁹(100-digit number)
23046410559233942557…96196939797081620479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.609 Γ— 10⁹⁹(100-digit number)
46092821118467885114…92393879594163240959
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2634621

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 5343387cfe064608ab39207dbb5958832b28df58882c0d55c4292827ac4722d7

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 #2,634,621 on Chainz β†—
Circulating Supply:57,982,052 XPMΒ·at block #6,842,206 Β· updates every 60s
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