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Block #226,813

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/25/2013, 11:50:38 AM Β· Difficulty 9.9360 Β· 6,597,719 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
866e27e6d5fce84d81c582e0068e43a64c0ca901eae4752d50cb14dc03c55278
View on Chainz β†—

Height

#226,813

Difficulty

9.935950

Transactions

3

Size

798 B

Version

2

Bits

09ef9a70

Nonce

277,175

Timestamp

10/25/2013, 11:50:38 AM

Confirmations

6,597,719

Merkle Root

dfa9884d46867dcb3d983f6a078dc29f4fa8c0ccdd084e0d49c4973720127663
Transactions (3)
Coinbase07c73250d4c35a…bcc9dee25a538c
1 in β†’ 1 out10.1300 XPM109 B
ATS83Fku…6dGV7DQk
6fa9d0d1cdaedf…a41df49e9e1f7b
2 in β†’ 2 out13.3096 XPM373 B
AWc1hWLq…cn2tLdqMALL6BtTJ…cp6j3qpk
03045a276ebe14…bdd8cae67345d6
1 in β†’ 2 out8.0215 XPM227 B
AbShu9Q7…L8C91NfMAXxR7fw2…1GRdKyfM
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.

3.386 Γ— 10⁹³(94-digit number)
33864602301456906868…95648806641268126510
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
3.386 Γ— 10⁹³(94-digit number)
33864602301456906868…95648806641268126511
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.772 Γ— 10⁹³(94-digit number)
67729204602913813737…91297613282536253021
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.354 Γ— 10⁹⁴(95-digit number)
13545840920582762747…82595226565072506041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.709 Γ— 10⁹⁴(95-digit number)
27091681841165525494…65190453130145012081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.418 Γ— 10⁹⁴(95-digit number)
54183363682331050989…30380906260290024161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.083 Γ— 10⁹⁡(96-digit number)
10836672736466210197…60761812520580048321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.167 Γ— 10⁹⁡(96-digit number)
21673345472932420395…21523625041160096641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.334 Γ— 10⁹⁡(96-digit number)
43346690945864840791…43047250082320193281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.669 Γ— 10⁹⁡(96-digit number)
86693381891729681583…86094500164640386561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.733 Γ— 10⁹⁢(97-digit number)
17338676378345936316…72189000329280773121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.467 Γ— 10⁹⁢(97-digit number)
34677352756691872633…44378000658561546241
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 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
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 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 226813

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 866e27e6d5fce84d81c582e0068e43a64c0ca901eae4752d50cb14dc03c55278

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 #226,813 on Chainz β†—
Circulating Supply:57,840,321 XPMΒ·at block #6,824,531 Β· updates every 60s
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