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Home/Chain Registry/Block #2,148,800

Block #2,148,800

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 6/6/2017, 4:56:06 PM Β· Difficulty 10.8958 Β· 4,694,014 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3536af273f949889f3d2e27a773c83aab8abcdd66bb36412f94b9a93188e0fce
View on Chainz β†—

Difficulty

10.895801

Transactions

1

Size

198 B

Version

2

Bits

0ae55332

Nonce

980,484,089

Timestamp

6/6/2017, 4:56:06 PM

Confirmations

4,694,014

Merkle Root

2e0d080416245f92b7b5e4351a9203efb9c371fdbb39c6d8d9482842805804e0
Transactions (1)
Coinbase2e0d080416245f…482842805804e0
1 in β†’ 1 out8.4100 XPM109 B
AJUkWRjS…E6UrEqjB
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.

1.242 Γ— 10⁹²(93-digit number)
12429747841806361338…29318343426252662800
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
1.242 Γ— 10⁹²(93-digit number)
12429747841806361338…29318343426252662799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.485 Γ— 10⁹²(93-digit number)
24859495683612722677…58636686852505325599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.971 Γ— 10⁹²(93-digit number)
49718991367225445354…17273373705010651199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.943 Γ— 10⁹²(93-digit number)
99437982734450890709…34546747410021302399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.988 Γ— 10⁹³(94-digit number)
19887596546890178141…69093494820042604799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.977 Γ— 10⁹³(94-digit number)
39775193093780356283…38186989640085209599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.955 Γ— 10⁹³(94-digit number)
79550386187560712567…76373979280170419199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.591 Γ— 10⁹⁴(95-digit number)
15910077237512142513…52747958560340838399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.182 Γ— 10⁹⁴(95-digit number)
31820154475024285026…05495917120681676799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.364 Γ— 10⁹⁴(95-digit number)
63640308950048570053…10991834241363353599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.272 Γ— 10⁹⁡(96-digit number)
12728061790009714010…21983668482726707199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
2.545 Γ— 10⁹⁡(96-digit number)
25456123580019428021…43967336965453414399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2148800

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 3536af273f949889f3d2e27a773c83aab8abcdd66bb36412f94b9a93188e0fce

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 #2,148,800 on Chainz β†—
Circulating Supply:57,986,852 XPMΒ·at block #6,842,813 Β· updates every 60s
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