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Home/Chain Registry/Block #2,725,215

Block #2,725,215

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/28/2018, 1:35:54 PM Β· Difficulty 11.6206 Β· 4,118,124 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
579df6a52489c997d57e942211a679be100f294199cce916f82f776b919b1c2a
View on Chainz β†—

Difficulty

11.620634

Transactions

1

Size

200 B

Version

2

Bits

0b9ee1e2

Nonce

262,188,165

Timestamp

6/28/2018, 1:35:54 PM

Confirmations

4,118,124

Merkle Root

4534262595e40b71212b0df91276efc13bb94fbcbaca2bfb7445b478969339ad
Transactions (1)
Coinbase4534262595e40b…45b478969339ad
1 in β†’ 1 out7.3900 XPM110 B
AJ1jF2XH…t3yBB3vw
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.

1.849 Γ— 10⁹⁴(95-digit number)
18490773204173226678…33316188178674530880
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
1.849 Γ— 10⁹⁴(95-digit number)
18490773204173226678…33316188178674530879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.698 Γ— 10⁹⁴(95-digit number)
36981546408346453357…66632376357349061759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.396 Γ— 10⁹⁴(95-digit number)
73963092816692906714…33264752714698123519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.479 Γ— 10⁹⁡(96-digit number)
14792618563338581342…66529505429396247039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.958 Γ— 10⁹⁡(96-digit number)
29585237126677162685…33059010858792494079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.917 Γ— 10⁹⁡(96-digit number)
59170474253354325371…66118021717584988159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.183 Γ— 10⁹⁢(97-digit number)
11834094850670865074…32236043435169976319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.366 Γ— 10⁹⁢(97-digit number)
23668189701341730148…64472086870339952639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.733 Γ— 10⁹⁢(97-digit number)
47336379402683460297…28944173740679905279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.467 Γ— 10⁹⁢(97-digit number)
94672758805366920594…57888347481359810559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.893 Γ— 10⁹⁷(98-digit number)
18934551761073384118…15776694962719621119
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 2725215

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 579df6a52489c997d57e942211a679be100f294199cce916f82f776b919b1c2a

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 #2,725,215 on Chainz β†—
Circulating Supply:57,991,072 XPMΒ·at block #6,843,338 Β· updates every 60s
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