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Block #199,728

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/8/2013, 1:44:44 PM Β· Difficulty 9.8880 Β· 6,595,784 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
40b20be855107a85cbae1f1c1641c3a22d37ee24daa62d0854723582e40e4cd2
View on Chainz β†—

Height

#199,728

Difficulty

9.888000

Transactions

1

Size

201 B

Version

2

Bits

09e353fe

Nonce

131,441

Timestamp

10/8/2013, 1:44:44 PM

Confirmations

6,595,784

Merkle Root

5bc8d69a58a23d82abfdea83e78083cb110648a420c8f6e875482a55446ff762
Transactions (1)
Coinbase5bc8d69a58a23d…482a55446ff762
1 in β†’ 1 out10.2100 XPM110 B
AFvfCa1W…3pZgbFWa
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.

2.524 Γ— 10⁹⁢(97-digit number)
25241241993477700813…26104507264688670080
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
2.524 Γ— 10⁹⁢(97-digit number)
25241241993477700813…26104507264688670081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.048 Γ— 10⁹⁢(97-digit number)
50482483986955401627…52209014529377340161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.009 Γ— 10⁹⁷(98-digit number)
10096496797391080325…04418029058754680321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.019 Γ— 10⁹⁷(98-digit number)
20192993594782160650…08836058117509360641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.038 Γ— 10⁹⁷(98-digit number)
40385987189564321301…17672116235018721281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.077 Γ— 10⁹⁷(98-digit number)
80771974379128642603…35344232470037442561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.615 Γ— 10⁹⁸(99-digit number)
16154394875825728520…70688464940074885121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.230 Γ— 10⁹⁸(99-digit number)
32308789751651457041…41376929880149770241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.461 Γ— 10⁹⁸(99-digit number)
64617579503302914083…82753859760299540481
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 199728

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 40b20be855107a85cbae1f1c1641c3a22d37ee24daa62d0854723582e40e4cd2

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 #199,728 on Chainz β†—
Circulating Supply:57,608,159 XPMΒ·at block #6,795,511 Β· updates every 60s
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