XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #155,543

Block #155,543

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/8/2013, 9:53:13 AM Β· Difficulty 9.8657 Β· 6,669,870 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3e86a6c720d4cfe2041a23ac0b97f51f70bc822dc7d48851445564f7447ebb61
View on Chainz β†—

Height

#155,543

Difficulty

9.865683

Transactions

1

Size

199 B

Version

2

Bits

09dd9d6e

Nonce

32,328

Timestamp

9/8/2013, 9:53:13 AM

Confirmations

6,669,870

Merkle Root

dfda5e35469adca06d172f3f8b8d2aa8f978ac224d62906e7f4b834a65324ac5
Transactions (1)
Coinbasedfda5e35469adc…4b834a65324ac5
1 in β†’ 1 out10.2600 XPM109 B
AaUeTZRc…gavZEn94
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.

2.242 Γ— 10⁹⁡(96-digit number)
22429343035397949602…94844654235544584560
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
2.242 Γ— 10⁹⁡(96-digit number)
22429343035397949602…94844654235544584561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.485 Γ— 10⁹⁡(96-digit number)
44858686070795899204…89689308471089169121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.971 Γ— 10⁹⁡(96-digit number)
89717372141591798408…79378616942178338241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.794 Γ— 10⁹⁢(97-digit number)
17943474428318359681…58757233884356676481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.588 Γ— 10⁹⁢(97-digit number)
35886948856636719363…17514467768713352961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.177 Γ— 10⁹⁢(97-digit number)
71773897713273438727…35028935537426705921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.435 Γ— 10⁹⁷(98-digit number)
14354779542654687745…70057871074853411841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.870 Γ— 10⁹⁷(98-digit number)
28709559085309375490…40115742149706823681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.741 Γ— 10⁹⁷(98-digit number)
57419118170618750981…80231484299413647361
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 155543

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 3e86a6c720d4cfe2041a23ac0b97f51f70bc822dc7d48851445564f7447ebb61

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 #155,543 on Chainz β†—
Circulating Supply:57,847,404 XPMΒ·at block #6,825,412 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