XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #105,265

Block #105,265

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2013, 10:46:53 AM Β· Difficulty 9.5797 Β· 6,689,310 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2f751b1fd2a7d17bd0e0e2431b84ae049a89c228e8772c59685ce880de0763a9
View on Chainz β†—

Height

#105,265

Difficulty

9.579681

Transactions

1

Size

200 B

Version

2

Bits

099465fd

Nonce

4,505

Timestamp

8/8/2013, 10:46:53 AM

Confirmations

6,689,310

Merkle Root

a715beca485d897aa7f295fd55c10cf70cece880358a48b6f722a56217bdbdde
Transactions (1)
Coinbasea715beca485d89…22a56217bdbdde
1 in β†’ 1 out10.8800 XPM109 B
ASXW8s4r…LM8vqY9U
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.

4.905 Γ— 10⁹⁢(97-digit number)
49054104475275137230…35723768215851301810
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.905 Γ— 10⁹⁢(97-digit number)
49054104475275137230…35723768215851301809
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.810 Γ— 10⁹⁢(97-digit number)
98108208950550274461…71447536431702603619
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.962 Γ— 10⁹⁷(98-digit number)
19621641790110054892…42895072863405207239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.924 Γ— 10⁹⁷(98-digit number)
39243283580220109784…85790145726810414479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.848 Γ— 10⁹⁷(98-digit number)
78486567160440219569…71580291453620828959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.569 Γ— 10⁹⁸(99-digit number)
15697313432088043913…43160582907241657919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.139 Γ— 10⁹⁸(99-digit number)
31394626864176087827…86321165814483315839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.278 Γ— 10⁹⁸(99-digit number)
62789253728352175655…72642331628966631679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.255 Γ— 10⁹⁹(100-digit number)
12557850745670435131…45284663257933263359
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 105265

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 2f751b1fd2a7d17bd0e0e2431b84ae049a89c228e8772c59685ce880de0763a9

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 #105,265 on Chainz β†—
Circulating Supply:57,600,645 XPMΒ·at block #6,794,574 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.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK