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Home/Chain Registry/Block #2,174,622

Block #2,174,622

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/24/2017, 12:30:56 AM Β· Difficulty 10.9133 Β· 4,656,396 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3325b2208d5fc1c248be18f92d452374250c1ee5fa1369c88c4689fbf269543f
View on Chainz β†—

Difficulty

10.913328

Transactions

1

Size

199 B

Version

2

Bits

0ae9cfe0

Nonce

1,518,085,373

Timestamp

6/24/2017, 12:30:56 AM

Confirmations

4,656,396

Merkle Root

da4f7ccea1fca634a886bfc0c606be9530f22b4573dcc052f1e44918fb5aec15
Transactions (1)
Coinbaseda4f7ccea1fca6…e44918fb5aec15
1 in β†’ 1 out8.3800 XPM109 B
AaMocyoS…v16oL5Sa
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.

1.580 Γ— 10⁹⁡(96-digit number)
15807622617593965554…03367136026358792320
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
1.580 Γ— 10⁹⁡(96-digit number)
15807622617593965554…03367136026358792319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.161 Γ— 10⁹⁡(96-digit number)
31615245235187931109…06734272052717584639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.323 Γ— 10⁹⁡(96-digit number)
63230490470375862218…13468544105435169279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.264 Γ— 10⁹⁢(97-digit number)
12646098094075172443…26937088210870338559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.529 Γ— 10⁹⁢(97-digit number)
25292196188150344887…53874176421740677119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.058 Γ— 10⁹⁢(97-digit number)
50584392376300689775…07748352843481354239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.011 Γ— 10⁹⁷(98-digit number)
10116878475260137955…15496705686962708479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.023 Γ— 10⁹⁷(98-digit number)
20233756950520275910…30993411373925416959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.046 Γ— 10⁹⁷(98-digit number)
40467513901040551820…61986822747850833919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.093 Γ— 10⁹⁷(98-digit number)
80935027802081103640…23973645495701667839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2174622

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 3325b2208d5fc1c248be18f92d452374250c1ee5fa1369c88c4689fbf269543f

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 #2,174,622 on Chainz β†—
Circulating Supply:57,892,285 XPMΒ·at block #6,831,017 Β· updates every 60s
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