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Home/Chain Registry/Block #2,223,136

Block #2,223,136

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/26/2017, 3:51:26 AM Β· Difficulty 10.9458 Β· 4,619,751 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
733dd04fe34b63e942b21bc3d4a6d1b983e7e320b704cf37416d9a90b78bbe89
View on Chainz β†—

Difficulty

10.945846

Transactions

2

Size

425 B

Version

2

Bits

0af222f9

Nonce

2,037,574,787

Timestamp

7/26/2017, 3:51:26 AM

Confirmations

4,619,751

Merkle Root

8eca1287c9542b028e7c19cfe837e8cf63a63ed60031c7c6ab52125d4d88e827
Transactions (2)
Coinbase619b6a3d1c9617…03cf8d1deccb10
1 in β†’ 1 out8.3400 XPM109 B
Ab4ZhsvK…4uweeyX7
58c6e10c4db9af…7bcbbb53c80cac
1 in β†’ 2 out0.2805 XPM226 B
AbSzLKZ5…aBJjMakRAZ2Z7Rs3…faiXxEwr
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.

3.983 Γ— 10⁹³(94-digit number)
39838995751808304305…56125465262967678950
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
3.983 Γ— 10⁹³(94-digit number)
39838995751808304305…56125465262967678951
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.967 Γ— 10⁹³(94-digit number)
79677991503616608610…12250930525935357901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.593 Γ— 10⁹⁴(95-digit number)
15935598300723321722…24501861051870715801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.187 Γ— 10⁹⁴(95-digit number)
31871196601446643444…49003722103741431601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.374 Γ— 10⁹⁴(95-digit number)
63742393202893286888…98007444207482863201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.274 Γ— 10⁹⁡(96-digit number)
12748478640578657377…96014888414965726401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.549 Γ— 10⁹⁡(96-digit number)
25496957281157314755…92029776829931452801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.099 Γ— 10⁹⁡(96-digit number)
50993914562314629510…84059553659862905601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.019 Γ— 10⁹⁢(97-digit number)
10198782912462925902…68119107319725811201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.039 Γ— 10⁹⁢(97-digit number)
20397565824925851804…36238214639451622401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second 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
UncommonChain length 10
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2223136

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 733dd04fe34b63e942b21bc3d4a6d1b983e7e320b704cf37416d9a90b78bbe89

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 #2,223,136 on Chainz β†—
Circulating Supply:57,987,442 XPMΒ·at block #6,842,886 Β· updates every 60s
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