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Block #2,582,781

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/24/2018, 11:07:56 AM Β· Difficulty 11.1430 Β· 4,257,838 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c7db2f282baf52b9d708f4b0d5b519f4df91a757579586f347d75ecd6905871d
View on Chainz β†—

Difficulty

11.143018

Transactions

1

Size

200 B

Version

2

Bits

0b249cdc

Nonce

344,377,301

Timestamp

3/24/2018, 11:07:56 AM

Confirmations

4,257,838

Merkle Root

bdd5b0c54cae3bb9a4dba8fa77c0c65a9201d88366e870c5884abadeaf9d0299
Transactions (1)
Coinbasebdd5b0c54cae3b…4abadeaf9d0299
1 in β†’ 1 out8.0400 XPM110 B
AKzGCHx9…pDGSAy41
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.

1.365 Γ— 10⁹⁡(96-digit number)
13656439748030492667…22451044541093097920
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
1.365 Γ— 10⁹⁡(96-digit number)
13656439748030492667…22451044541093097919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.731 Γ— 10⁹⁡(96-digit number)
27312879496060985335…44902089082186195839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.462 Γ— 10⁹⁡(96-digit number)
54625758992121970671…89804178164372391679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.092 Γ— 10⁹⁢(97-digit number)
10925151798424394134…79608356328744783359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.185 Γ— 10⁹⁢(97-digit number)
21850303596848788268…59216712657489566719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.370 Γ— 10⁹⁢(97-digit number)
43700607193697576537…18433425314979133439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.740 Γ— 10⁹⁢(97-digit number)
87401214387395153074…36866850629958266879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.748 Γ— 10⁹⁷(98-digit number)
17480242877479030614…73733701259916533759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.496 Γ— 10⁹⁷(98-digit number)
34960485754958061229…47467402519833067519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.992 Γ— 10⁹⁷(98-digit number)
69920971509916122459…94934805039666135039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.398 Γ— 10⁹⁸(99-digit number)
13984194301983224491…89869610079332270079
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 2582781

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 c7db2f282baf52b9d708f4b0d5b519f4df91a757579586f347d75ecd6905871d

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 #2,582,781 on Chainz β†—
Circulating Supply:57,969,290 XPMΒ·at block #6,840,618 Β· updates every 60s
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