XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #124,064

Block #124,064

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/19/2013, 10:29:44 AM Β· Difficulty 9.7681 Β· 6,689,808 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9055c0c79db852e0ed20b48fe2e4a473033e94d0329deae3d2833ccf3f4b6d21
View on Chainz β†—

Height

#124,064

Difficulty

9.768115

Transactions

1

Size

200 B

Version

2

Bits

09c4a32d

Nonce

719,249

Timestamp

8/19/2013, 10:29:44 AM

Confirmations

6,689,808

Merkle Root

a01a5a68f21d85709cfff5f951f913b8a952333e7c640bd0b3ff485e83b3d080
Transactions (1)
Coinbasea01a5a68f21d85…ff485e83b3d080
1 in β†’ 1 out10.4600 XPM109 B
ATjkewJn…jRotsgMp
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.

1.491 Γ— 10⁹⁢(97-digit number)
14917977014321442389…23228417138675502660
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
1.491 Γ— 10⁹⁢(97-digit number)
14917977014321442389…23228417138675502659
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.983 Γ— 10⁹⁢(97-digit number)
29835954028642884779…46456834277351005319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.967 Γ— 10⁹⁢(97-digit number)
59671908057285769559…92913668554702010639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.193 Γ— 10⁹⁷(98-digit number)
11934381611457153911…85827337109404021279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.386 Γ— 10⁹⁷(98-digit number)
23868763222914307823…71654674218808042559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.773 Γ— 10⁹⁷(98-digit number)
47737526445828615647…43309348437616085119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.547 Γ— 10⁹⁷(98-digit number)
95475052891657231295…86618696875232170239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.909 Γ— 10⁹⁸(99-digit number)
19095010578331446259…73237393750464340479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.819 Γ— 10⁹⁸(99-digit number)
38190021156662892518…46474787500928680959
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 124064

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 9055c0c79db852e0ed20b48fe2e4a473033e94d0329deae3d2833ccf3f4b6d21

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 #124,064 on Chainz β†—
Circulating Supply:57,755,050 XPMΒ·at block #6,813,871 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