XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #373,138

Block #373,138

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/24/2014, 2:49:33 AM Β· Difficulty 10.4245 Β· 6,452,447 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
93354fc07d2199a11c3b6014cb312bd652bb0c2eb31e6af46c24e414da4f544b
View on Chainz β†—

Height

#373,138

Difficulty

10.424500

Transactions

1

Size

200 B

Version

2

Bits

0a6cac08

Nonce

340,611

Timestamp

1/24/2014, 2:49:33 AM

Confirmations

6,452,447

Merkle Root

b555454403ac6185a4b4bbf17ab001caeb11f5879400146aef5511f7f20cbca0
Transactions (1)
Coinbaseb555454403ac61…5511f7f20cbca0
1 in β†’ 1 out9.1900 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.012 Γ— 10⁹⁴(95-digit number)
10120450731150765091…88142516384892562710
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
1.012 Γ— 10⁹⁴(95-digit number)
10120450731150765091…88142516384892562709
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.024 Γ— 10⁹⁴(95-digit number)
20240901462301530183…76285032769785125419
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.048 Γ— 10⁹⁴(95-digit number)
40481802924603060367…52570065539570250839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.096 Γ— 10⁹⁴(95-digit number)
80963605849206120734…05140131079140501679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.619 Γ— 10⁹⁡(96-digit number)
16192721169841224146…10280262158281003359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.238 Γ— 10⁹⁡(96-digit number)
32385442339682448293…20560524316562006719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.477 Γ— 10⁹⁡(96-digit number)
64770884679364896587…41121048633124013439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.295 Γ— 10⁹⁢(97-digit number)
12954176935872979317…82242097266248026879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.590 Γ— 10⁹⁢(97-digit number)
25908353871745958635…64484194532496053759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.181 Γ— 10⁹⁢(97-digit number)
51816707743491917270…28968389064992107519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.036 Γ— 10⁹⁷(98-digit number)
10363341548698383454…57936778129984215039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 373138

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 93354fc07d2199a11c3b6014cb312bd652bb0c2eb31e6af46c24e414da4f544b

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 #373,138 on Chainz β†—
Circulating Supply:57,848,779 XPMΒ·at block #6,825,584 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