XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #205,676

Block #205,676

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/12/2013, 7:35:14 AM Β· Difficulty 9.9001 Β· 6,631,178 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
69f28d621888e6b4063345a0d0b61c2095fc787d5289a5e9902b4814b35adb29
View on Chainz β†—

Height

#205,676

Difficulty

9.900119

Transactions

1

Size

199 B

Version

2

Bits

09e66e2e

Nonce

126,429

Timestamp

10/12/2013, 7:35:14 AM

Confirmations

6,631,178

Merkle Root

8dfcc952e66f726252b883e95eca9b9e12973186ac5811ec405d39dbdc1b73b0
Transactions (1)
Coinbase8dfcc952e66f72…5d39dbdc1b73b0
1 in β†’ 1 out10.1900 XPM109 B
ANehrGnB…LZL3TANF
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.

3.409 Γ— 10⁹⁴(95-digit number)
34095005511726915571…42983665703355964800
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
3.409 Γ— 10⁹⁴(95-digit number)
34095005511726915571…42983665703355964801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.819 Γ— 10⁹⁴(95-digit number)
68190011023453831143…85967331406711929601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.363 Γ— 10⁹⁡(96-digit number)
13638002204690766228…71934662813423859201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.727 Γ— 10⁹⁡(96-digit number)
27276004409381532457…43869325626847718401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.455 Γ— 10⁹⁡(96-digit number)
54552008818763064914…87738651253695436801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.091 Γ— 10⁹⁢(97-digit number)
10910401763752612982…75477302507390873601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.182 Γ— 10⁹⁢(97-digit number)
21820803527505225965…50954605014781747201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.364 Γ— 10⁹⁢(97-digit number)
43641607055010451931…01909210029563494401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.728 Γ— 10⁹⁢(97-digit number)
87283214110020903863…03818420059126988801
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 205676

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 69f28d621888e6b4063345a0d0b61c2095fc787d5289a5e9902b4814b35adb29

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 #205,676 on Chainz β†—
Circulating Supply:57,939,120 XPMΒ·at block #6,836,853 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