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Home/Chain Registry/Block #164,828

Block #164,828

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/14/2013, 9:59:31 PM Β· Difficulty 9.8639 Β· 6,635,597 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d80dc24d6ac94045f9dac39808fccbb91f9abf2f28cc22e724dfd85c0e7f497b
View on Chainz β†—

Height

#164,828

Difficulty

9.863878

Transactions

2

Size

573 B

Version

2

Bits

09dd2719

Nonce

47,499

Timestamp

9/14/2013, 9:59:31 PM

Confirmations

6,635,597

Merkle Root

a8ca81416659d8fbf373a57a917657d328032fca1c30311162c6493c4d92f674
Transactions (2)
Coinbasec5cbd3570302a0…eef466e14550dd
1 in β†’ 1 out10.2700 XPM109 B
AbgqPxeb…Y2jPnbse
78793557004e44…7ec92c0272896d
2 in β†’ 2 out209.9900 XPM373 B
AP5SiJo4…j7A7ZeVBAeF8cxmP…TZsMgEgt
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.

1.417 Γ— 10⁹⁢(97-digit number)
14179020647547000946…91254836431043333120
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
1.417 Γ— 10⁹⁢(97-digit number)
14179020647547000946…91254836431043333121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.835 Γ— 10⁹⁢(97-digit number)
28358041295094001893…82509672862086666241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.671 Γ— 10⁹⁢(97-digit number)
56716082590188003787…65019345724173332481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.134 Γ— 10⁹⁷(98-digit number)
11343216518037600757…30038691448346664961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.268 Γ— 10⁹⁷(98-digit number)
22686433036075201514…60077382896693329921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.537 Γ— 10⁹⁷(98-digit number)
45372866072150403029…20154765793386659841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.074 Γ— 10⁹⁷(98-digit number)
90745732144300806059…40309531586773319681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.814 Γ— 10⁹⁸(99-digit number)
18149146428860161211…80619063173546639361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.629 Γ— 10⁹⁸(99-digit number)
36298292857720322423…61238126347093278721
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 164828

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 d80dc24d6ac94045f9dac39808fccbb91f9abf2f28cc22e724dfd85c0e7f497b

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 #164,828 on Chainz β†—
Circulating Supply:57,647,465 XPMΒ·at block #6,800,424 Β· updates every 60s
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