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Home/Chain Registry/Block #2,582,783

Block #2,582,783

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/24/2018, 11:09:26 AM Β· Difficulty 11.1432 Β· 4,254,337 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
51e0d2a1b0f54d809702f46ad9477e34d973663e77996c8424a7f5b5d0d3f797
View on Chainz β†—

Difficulty

11.143203

Transactions

1

Size

200 B

Version

2

Bits

0b24a8ef

Nonce

68,022,464

Timestamp

3/24/2018, 11:09:26 AM

Confirmations

4,254,337

Merkle Root

a594642af024dfd4c5250e170fc9b3d8e58d1db22b44b94d25d88f911b1c7416
Transactions (1)
Coinbasea594642af024df…d88f911b1c7416
1 in β†’ 1 out8.0400 XPM110 B
AVD5Zs2n…L6QwcXim
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.

2.310 Γ— 10⁹⁡(96-digit number)
23103602190800127918…89371118699996101120
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
2.310 Γ— 10⁹⁡(96-digit number)
23103602190800127918…89371118699996101121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.620 Γ— 10⁹⁡(96-digit number)
46207204381600255836…78742237399992202241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.241 Γ— 10⁹⁡(96-digit number)
92414408763200511672…57484474799984404481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.848 Γ— 10⁹⁢(97-digit number)
18482881752640102334…14968949599968808961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.696 Γ— 10⁹⁢(97-digit number)
36965763505280204668…29937899199937617921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.393 Γ— 10⁹⁢(97-digit number)
73931527010560409337…59875798399875235841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.478 Γ— 10⁹⁷(98-digit number)
14786305402112081867…19751596799750471681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.957 Γ— 10⁹⁷(98-digit number)
29572610804224163735…39503193599500943361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.914 Γ— 10⁹⁷(98-digit number)
59145221608448327470…79006387199001886721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.182 Γ— 10⁹⁸(99-digit number)
11829044321689665494…58012774398003773441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.365 Γ— 10⁹⁸(99-digit number)
23658088643379330988…16025548796007546881
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 2582783

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 51e0d2a1b0f54d809702f46ad9477e34d973663e77996c8424a7f5b5d0d3f797

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 #2,582,783 on Chainz β†—
Circulating Supply:57,941,269 XPMΒ·at block #6,837,119 Β· updates every 60s
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