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Block #199,279

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/8/2013, 6:56:21 AM Β· Difficulty 9.8871 Β· 6,596,550 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bf7e684e994443a43d10eda855a9ebf24d8ed9ff2c5108462e21ff4961cec076
View on Chainz β†—

Height

#199,279

Difficulty

9.887076

Transactions

1

Size

208 B

Version

2

Bits

09e31764

Nonce

4

Timestamp

10/8/2013, 6:56:21 AM

Confirmations

6,596,550

Merkle Root

4123886c4feafb3fea8ff79b21e8e4805dd1a174845748e236023dc935656cab
Transactions (1)
Coinbase4123886c4feafb…023dc935656cab
1 in β†’ 1 out10.2100 XPM116 B
AcLBm5Z9…S683d7c3
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.

3.868 Γ— 10⁹⁹(100-digit number)
38687283305786558965…09452266333203282240
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
3.868 Γ— 10⁹⁹(100-digit number)
38687283305786558965…09452266333203282241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.737 Γ— 10⁹⁹(100-digit number)
77374566611573117931…18904532666406564481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.547 Γ— 10¹⁰⁰(101-digit number)
15474913322314623586…37809065332813128961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.094 Γ— 10¹⁰⁰(101-digit number)
30949826644629247172…75618130665626257921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.189 Γ— 10¹⁰⁰(101-digit number)
61899653289258494345…51236261331252515841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.237 Γ— 10¹⁰¹(102-digit number)
12379930657851698869…02472522662505031681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.475 Γ— 10¹⁰¹(102-digit number)
24759861315703397738…04945045325010063361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.951 Γ— 10¹⁰¹(102-digit number)
49519722631406795476…09890090650020126721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.903 Γ— 10¹⁰¹(102-digit number)
99039445262813590952…19780181300040253441
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 199279

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 bf7e684e994443a43d10eda855a9ebf24d8ed9ff2c5108462e21ff4961cec076

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 #199,279 on Chainz β†—
Circulating Supply:57,610,715 XPMΒ·at block #6,795,828 Β· updates every 60s
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