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Home/Chain Registry/Block #2,820,646

Block #2,820,646

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/2/2018, 1:08:04 AM Β· Difficulty 11.7003 Β· 4,024,624 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d2e8a46449926c686d76ace164877291284e429ec4f1a7d5ba4c0c5d7958f4dd
View on Chainz β†—

Difficulty

11.700321

Transactions

1

Size

201 B

Version

2

Bits

0bb34839

Nonce

583,152,259

Timestamp

9/2/2018, 1:08:04 AM

Confirmations

4,024,624

Merkle Root

7fdced21001df36cc818d7bd6bbcf4d0362e5bca95959354738f2d95044ae1fd
Transactions (1)
Coinbase7fdced21001df3…8f2d95044ae1fd
1 in β†’ 1 out7.2900 XPM110 B
AXnqwuuM…4Jw9Aza4
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.

1.605 Γ— 10⁹⁸(99-digit number)
16058125078572117004…81505827584073113600
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
1.605 Γ— 10⁹⁸(99-digit number)
16058125078572117004…81505827584073113601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.211 Γ— 10⁹⁸(99-digit number)
32116250157144234008…63011655168146227201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.423 Γ— 10⁹⁸(99-digit number)
64232500314288468016…26023310336292454401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.284 Γ— 10⁹⁹(100-digit number)
12846500062857693603…52046620672584908801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.569 Γ— 10⁹⁹(100-digit number)
25693000125715387206…04093241345169817601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.138 Γ— 10⁹⁹(100-digit number)
51386000251430774413…08186482690339635201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.027 Γ— 10¹⁰⁰(101-digit number)
10277200050286154882…16372965380679270401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.055 Γ— 10¹⁰⁰(101-digit number)
20554400100572309765…32745930761358540801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.110 Γ— 10¹⁰⁰(101-digit number)
41108800201144619530…65491861522717081601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.221 Γ— 10¹⁰⁰(101-digit number)
82217600402289239061…30983723045434163201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.644 Γ— 10¹⁰¹(102-digit number)
16443520080457847812…61967446090868326401
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 2820646

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 d2e8a46449926c686d76ace164877291284e429ec4f1a7d5ba4c0c5d7958f4dd

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 #2,820,646 on Chainz β†—
Circulating Supply:58,006,595 XPMΒ·at block #6,845,269 Β· updates every 60s
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