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Home/Chain Registry/Block #2,820,913

Block #2,820,913

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/2/2018, 5:38:21 AM Β· Difficulty 11.7001 Β· 4,021,022 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fc9a770518f746ae9b4496f0945e1ce7e34eac861654ed22d7ed75e0060581e5
View on Chainz β†—

Difficulty

11.700119

Transactions

1

Size

201 B

Version

2

Bits

0bb33b02

Nonce

188,621,116

Timestamp

9/2/2018, 5:38:21 AM

Confirmations

4,021,022

Merkle Root

c12de591ae2c435a5170d09ef2c1ca702e0df7fd0cf18643cd2edaba8c385771
Transactions (1)
Coinbasec12de591ae2c43…2edaba8c385771
1 in β†’ 1 out7.2900 XPM110 B
AYcGvAMP…S6LmKHxh
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.

2.624 Γ— 10⁹⁷(98-digit number)
26246547892050452420…42795283236760084480
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
2.624 Γ— 10⁹⁷(98-digit number)
26246547892050452420…42795283236760084481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.249 Γ— 10⁹⁷(98-digit number)
52493095784100904840…85590566473520168961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.049 Γ— 10⁹⁸(99-digit number)
10498619156820180968…71181132947040337921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.099 Γ— 10⁹⁸(99-digit number)
20997238313640361936…42362265894080675841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.199 Γ— 10⁹⁸(99-digit number)
41994476627280723872…84724531788161351681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.398 Γ— 10⁹⁸(99-digit number)
83988953254561447744…69449063576322703361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.679 Γ— 10⁹⁹(100-digit number)
16797790650912289548…38898127152645406721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.359 Γ— 10⁹⁹(100-digit number)
33595581301824579097…77796254305290813441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.719 Γ— 10⁹⁹(100-digit number)
67191162603649158195…55592508610581626881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.343 Γ— 10¹⁰⁰(101-digit number)
13438232520729831639…11185017221163253761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.687 Γ— 10¹⁰⁰(101-digit number)
26876465041459663278…22370034442326507521
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 2820913

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 fc9a770518f746ae9b4496f0945e1ce7e34eac861654ed22d7ed75e0060581e5

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 #2,820,913 on Chainz β†—
Circulating Supply:57,979,859 XPMΒ·at block #6,841,934 Β· updates every 60s
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