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Block #2,644,244

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 10:06:22 AM Β· Difficulty 11.7054 Β· 4,189,211 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3d2e46bbb3b60c3df9af475074f639e07aabf6dbea4bd18617a7f94a690ab5b9
View on Chainz β†—

Difficulty

11.705442

Transactions

1

Size

200 B

Version

2

Bits

0bb497d6

Nonce

26,759,355

Timestamp

5/2/2018, 10:06:22 AM

Confirmations

4,189,211

Merkle Root

62ca867de1befc831227cd6216d4739fc13691017e4e0897a5d3bbbd26ea72ff
Transactions (1)
Coinbase62ca867de1befc…d3bbbd26ea72ff
1 in β†’ 1 out7.2900 XPM110 B
APcoiecy…Hh35q5Dq
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.

4.303 Γ— 10⁹⁡(96-digit number)
43037877721694039000…37250376580802091360
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
4.303 Γ— 10⁹⁡(96-digit number)
43037877721694039000…37250376580802091359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.607 Γ— 10⁹⁡(96-digit number)
86075755443388078000…74500753161604182719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.721 Γ— 10⁹⁢(97-digit number)
17215151088677615600…49001506323208365439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.443 Γ— 10⁹⁢(97-digit number)
34430302177355231200…98003012646416730879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.886 Γ— 10⁹⁢(97-digit number)
68860604354710462400…96006025292833461759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.377 Γ— 10⁹⁷(98-digit number)
13772120870942092480…92012050585666923519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.754 Γ— 10⁹⁷(98-digit number)
27544241741884184960…84024101171333847039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.508 Γ— 10⁹⁷(98-digit number)
55088483483768369920…68048202342667694079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.101 Γ— 10⁹⁸(99-digit number)
11017696696753673984…36096404685335388159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.203 Γ— 10⁹⁸(99-digit number)
22035393393507347968…72192809370670776319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.407 Γ— 10⁹⁸(99-digit number)
44070786787014695936…44385618741341552639
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 2644244

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 3d2e46bbb3b60c3df9af475074f639e07aabf6dbea4bd18617a7f94a690ab5b9

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 #2,644,244 on Chainz β†—
Circulating Supply:57,911,839 XPMΒ·at block #6,833,454 Β· updates every 60s
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