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Block #164,830

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/14/2013, 9:59:50 PM Β· Difficulty 9.8639 Β· 6,662,006 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4bd653b41eca2588ebdf0c6544e9b385d6f7a3b1595ede5afd48629e50875c59
View on Chainz β†—

Height

#164,830

Difficulty

9.863921

Transactions

1

Size

198 B

Version

2

Bits

09dd29ef

Nonce

1,362

Timestamp

9/14/2013, 9:59:50 PM

Confirmations

6,662,006

Merkle Root

a467dad3048dc336fa08057232e9bd5647af35688bdb5af5354a007715ef33ea
Transactions (1)
Coinbasea467dad3048dc3…4a007715ef33ea
1 in β†’ 1 out10.2600 XPM109 B
AMCWARXQ…VyQK5P4T
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.

7.145 Γ— 10⁹²(93-digit number)
71455271701517994739…81445318059601216000
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
7.145 Γ— 10⁹²(93-digit number)
71455271701517994739…81445318059601216001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.429 Γ— 10⁹³(94-digit number)
14291054340303598947…62890636119202432001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.858 Γ— 10⁹³(94-digit number)
28582108680607197895…25781272238404864001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.716 Γ— 10⁹³(94-digit number)
57164217361214395791…51562544476809728001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.143 Γ— 10⁹⁴(95-digit number)
11432843472242879158…03125088953619456001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.286 Γ— 10⁹⁴(95-digit number)
22865686944485758316…06250177907238912001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.573 Γ— 10⁹⁴(95-digit number)
45731373888971516633…12500355814477824001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.146 Γ— 10⁹⁴(95-digit number)
91462747777943033266…25000711628955648001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.829 Γ— 10⁹⁡(96-digit number)
18292549555588606653…50001423257911296001
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 164830

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 4bd653b41eca2588ebdf0c6544e9b385d6f7a3b1595ede5afd48629e50875c59

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 #164,830 on Chainz β†—
Circulating Supply:57,858,854 XPMΒ·at block #6,826,835 Β· updates every 60s
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