XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #111,697

Block #111,697

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/11/2013, 2:22:19 PM Β· Difficulty 9.7119 Β· 6,713,937 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ca7731889e396a637736b594748296dc47b7bb6fdb768ad5b6d82b8a47f1684a
View on Chainz β†—

Height

#111,697

Difficulty

9.711863

Transactions

1

Size

200 B

Version

2

Bits

09b63ca4

Nonce

147,040

Timestamp

8/11/2013, 2:22:19 PM

Confirmations

6,713,937

Merkle Root

596842db520732f6ab034e8bfa72183e347e42a1bf9933ea1e2c6fbfabc928b4
Transactions (1)
Coinbase596842db520732…2c6fbfabc928b4
1 in β†’ 1 out10.5900 XPM109 B
AQaTLT75…AUY9M1Qv
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.

3.583 Γ— 10⁹⁢(97-digit number)
35830339772216016311…88724315129990847360
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
3.583 Γ— 10⁹⁢(97-digit number)
35830339772216016311…88724315129990847359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.166 Γ— 10⁹⁢(97-digit number)
71660679544432032623…77448630259981694719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.433 Γ— 10⁹⁷(98-digit number)
14332135908886406524…54897260519963389439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.866 Γ— 10⁹⁷(98-digit number)
28664271817772813049…09794521039926778879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.732 Γ— 10⁹⁷(98-digit number)
57328543635545626099…19589042079853557759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.146 Γ— 10⁹⁸(99-digit number)
11465708727109125219…39178084159707115519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.293 Γ— 10⁹⁸(99-digit number)
22931417454218250439…78356168319414231039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.586 Γ— 10⁹⁸(99-digit number)
45862834908436500879…56712336638828462079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.172 Γ— 10⁹⁸(99-digit number)
91725669816873001758…13424673277656924159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.834 Γ— 10⁹⁹(100-digit number)
18345133963374600351…26849346555313848319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 111697

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 ca7731889e396a637736b594748296dc47b7bb6fdb768ad5b6d82b8a47f1684a

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 #111,697 on Chainz β†—
Circulating Supply:57,849,176 XPMΒ·at block #6,825,633 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