XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #110,432

Block #110,432

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/10/2013, 11:06:06 PM Β· Difficulty 9.6912 Β· 6,716,188 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e6ca75834d256450b6074cc4f722f8f38cbf29d781a1a27c72978f6be81dc7ad
View on Chainz β†—

Height

#110,432

Difficulty

9.691189

Transactions

1

Size

200 B

Version

2

Bits

09b0f1c7

Nonce

232,269

Timestamp

8/10/2013, 11:06:06 PM

Confirmations

6,716,188

Merkle Root

911482d0c67c28573ed110cef5d1b2afaa742bcb105e3737b5dc7aa9a46adfe9
Transactions (1)
Coinbase911482d0c67c28…dc7aa9a46adfe9
1 in β†’ 1 out10.6300 XPM109 B
AGNF5FM1…n54CJy51
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.

4.160 Γ— 10⁹⁷(98-digit number)
41606778407725213857…05177010666045491620
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
4.160 Γ— 10⁹⁷(98-digit number)
41606778407725213857…05177010666045491619
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.321 Γ— 10⁹⁷(98-digit number)
83213556815450427714…10354021332090983239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.664 Γ— 10⁹⁸(99-digit number)
16642711363090085542…20708042664181966479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.328 Γ— 10⁹⁸(99-digit number)
33285422726180171085…41416085328363932959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.657 Γ— 10⁹⁸(99-digit number)
66570845452360342171…82832170656727865919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.331 Γ— 10⁹⁹(100-digit number)
13314169090472068434…65664341313455731839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.662 Γ— 10⁹⁹(100-digit number)
26628338180944136868…31328682626911463679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.325 Γ— 10⁹⁹(100-digit number)
53256676361888273737…62657365253822927359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.065 Γ— 10¹⁰⁰(101-digit number)
10651335272377654747…25314730507645854719
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 110432

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 e6ca75834d256450b6074cc4f722f8f38cbf29d781a1a27c72978f6be81dc7ad

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 #110,432 on Chainz β†—
Circulating Supply:57,857,113 XPMΒ·at block #6,826,619 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