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Home/Chain Registry/Block #2,845,040

Block #2,845,040

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 9/18/2018, 3:32:13 PM Β· Difficulty 11.7288 Β· 3,998,231 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2e1e9bb537102872da2e54423671cfa774800c471d5efa6d4a6642fd0a109e43
View on Chainz β†—

Difficulty

11.728837

Transactions

1

Size

200 B

Version

2

Bits

0bba950c

Nonce

2,107,018,174

Timestamp

9/18/2018, 3:32:13 PM

Confirmations

3,998,231

Merkle Root

fb74199e8ef3accd3e235513ae3a5b0213edf57688003cab4531b9520385121e
Transactions (1)
Coinbasefb74199e8ef3ac…31b9520385121e
1 in β†’ 1 out7.2600 XPM110 B
AZtxQr2F…7grUWrUz
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.

1.848 Γ— 10⁹⁡(96-digit number)
18488560082199399396…51784756641089087120
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
1.848 Γ— 10⁹⁡(96-digit number)
18488560082199399396…51784756641089087119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.697 Γ— 10⁹⁡(96-digit number)
36977120164398798793…03569513282178174239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.395 Γ— 10⁹⁡(96-digit number)
73954240328797597586…07139026564356348479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.479 Γ— 10⁹⁢(97-digit number)
14790848065759519517…14278053128712696959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.958 Γ— 10⁹⁢(97-digit number)
29581696131519039034…28556106257425393919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.916 Γ— 10⁹⁢(97-digit number)
59163392263038078069…57112212514850787839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.183 Γ— 10⁹⁷(98-digit number)
11832678452607615613…14224425029701575679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.366 Γ— 10⁹⁷(98-digit number)
23665356905215231227…28448850059403151359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.733 Γ— 10⁹⁷(98-digit number)
47330713810430462455…56897700118806302719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.466 Γ— 10⁹⁷(98-digit number)
94661427620860924910…13795400237612605439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.893 Γ— 10⁹⁸(99-digit number)
18932285524172184982…27590800475225210879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
3.786 Γ— 10⁹⁸(99-digit number)
37864571048344369964…55181600950450421759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2845040

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 2e1e9bb537102872da2e54423671cfa774800c471d5efa6d4a6642fd0a109e43

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 #2,845,040 on Chainz β†—
Circulating Supply:57,990,542 XPMΒ·at block #6,843,270 Β· updates every 60s
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