XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #165,529

Block #165,529

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/15/2013, 8:39:42 AM Β· Difficulty 9.8656 Β· 6,659,504 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d35e721946691110e16640bac86b8be829537a9e74694a3d0d7af99ae9cb7a32
View on Chainz β†—

Height

#165,529

Difficulty

9.865554

Transactions

1

Size

200 B

Version

2

Bits

09dd94f3

Nonce

135,295

Timestamp

9/15/2013, 8:39:42 AM

Confirmations

6,659,504

Merkle Root

3221f7c3e82ddde5b358c03b21932902935455426d355c111a28e11a9f360d15
Transactions (1)
Coinbase3221f7c3e82ddd…28e11a9f360d15
1 in β†’ 1 out10.2600 XPM110 B
AKRz1T65…uAUbhMVc
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.

1.945 Γ— 10⁹⁡(96-digit number)
19456656336419292936…98926903981593408000
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
1.945 Γ— 10⁹⁡(96-digit number)
19456656336419292936…98926903981593408001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.891 Γ— 10⁹⁡(96-digit number)
38913312672838585872…97853807963186816001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.782 Γ— 10⁹⁡(96-digit number)
77826625345677171744…95707615926373632001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.556 Γ— 10⁹⁢(97-digit number)
15565325069135434348…91415231852747264001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.113 Γ— 10⁹⁢(97-digit number)
31130650138270868697…82830463705494528001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.226 Γ— 10⁹⁢(97-digit number)
62261300276541737395…65660927410989056001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.245 Γ— 10⁹⁷(98-digit number)
12452260055308347479…31321854821978112001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.490 Γ— 10⁹⁷(98-digit number)
24904520110616694958…62643709643956224001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.980 Γ— 10⁹⁷(98-digit number)
49809040221233389916…25287419287912448001
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 165529

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 d35e721946691110e16640bac86b8be829537a9e74694a3d0d7af99ae9cb7a32

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 #165,529 on Chainz β†—
Circulating Supply:57,844,347 XPMΒ·at block #6,825,032 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy