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Block #2,633,800

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/28/2018, 2:59:12 PM Β· Difficulty 11.2087 Β· 4,202,649 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5648b7c4c5cbdcebb9b0976542d369308b28b34d15d367ee0500ab5f9b8326e7
View on Chainz β†—

Difficulty

11.208673

Transactions

1

Size

200 B

Version

2

Bits

0b356b9e

Nonce

1,151,831,130

Timestamp

4/28/2018, 2:59:12 PM

Confirmations

4,202,649

Merkle Root

16c0133d96f0f7f6cabcfb8dbcb3bbb17a0c91100aac4a7b73a4562ba0be759c
Transactions (1)
Coinbase16c0133d96f0f7…a4562ba0be759c
1 in β†’ 1 out7.9500 XPM110 B
AdR8qwqt…rcZesXsL
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.

1.189 Γ— 10⁹⁴(95-digit number)
11895342869732321705…78900289710091243520
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
1.189 Γ— 10⁹⁴(95-digit number)
11895342869732321705…78900289710091243519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.379 Γ— 10⁹⁴(95-digit number)
23790685739464643411…57800579420182487039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.758 Γ— 10⁹⁴(95-digit number)
47581371478929286822…15601158840364974079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.516 Γ— 10⁹⁴(95-digit number)
95162742957858573645…31202317680729948159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.903 Γ— 10⁹⁡(96-digit number)
19032548591571714729…62404635361459896319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.806 Γ— 10⁹⁡(96-digit number)
38065097183143429458…24809270722919792639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.613 Γ— 10⁹⁡(96-digit number)
76130194366286858916…49618541445839585279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.522 Γ— 10⁹⁢(97-digit number)
15226038873257371783…99237082891679170559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.045 Γ— 10⁹⁢(97-digit number)
30452077746514743566…98474165783358341119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.090 Γ— 10⁹⁢(97-digit number)
60904155493029487133…96948331566716682239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.218 Γ— 10⁹⁷(98-digit number)
12180831098605897426…93896663133433364479
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 2633800

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 5648b7c4c5cbdcebb9b0976542d369308b28b34d15d367ee0500ab5f9b8326e7

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 #2,633,800 on Chainz β†—
Circulating Supply:57,935,862 XPMΒ·at block #6,836,448 Β· updates every 60s
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