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Home/Chain Registry/Block #2,285,073

Block #2,285,073

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/6/2017, 3:07:48 PM Β· Difficulty 10.9553 Β· 4,554,610 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3a5421d7125984791a1089a972885a7f59891e5419aa95e28f091133a8d12a4e
View on Chainz β†—

Difficulty

10.955336

Transactions

1

Size

200 B

Version

2

Bits

0af490e8

Nonce

1,407,027,753

Timestamp

9/6/2017, 3:07:48 PM

Confirmations

4,554,610

Merkle Root

7e178bed93534f4fe12060961d4ddcb1d9d40953ab2f10a1619ae93b0cbe8454
Transactions (1)
Coinbase7e178bed93534f…9ae93b0cbe8454
1 in β†’ 1 out8.3200 XPM110 B
AUPvb81T…FMWJHJVK
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.

1.382 Γ— 10⁹⁴(95-digit number)
13823327992948128393…18875857672365249000
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
1.382 Γ— 10⁹⁴(95-digit number)
13823327992948128393…18875857672365248999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.764 Γ— 10⁹⁴(95-digit number)
27646655985896256786…37751715344730497999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.529 Γ— 10⁹⁴(95-digit number)
55293311971792513572…75503430689460995999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.105 Γ— 10⁹⁡(96-digit number)
11058662394358502714…51006861378921991999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.211 Γ— 10⁹⁡(96-digit number)
22117324788717005428…02013722757843983999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.423 Γ— 10⁹⁡(96-digit number)
44234649577434010857…04027445515687967999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.846 Γ— 10⁹⁡(96-digit number)
88469299154868021715…08054891031375935999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.769 Γ— 10⁹⁢(97-digit number)
17693859830973604343…16109782062751871999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.538 Γ— 10⁹⁢(97-digit number)
35387719661947208686…32219564125503743999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.077 Γ— 10⁹⁢(97-digit number)
70775439323894417372…64439128251007487999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.415 Γ— 10⁹⁷(98-digit number)
14155087864778883474…28878256502014975999
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 2285073

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 3a5421d7125984791a1089a972885a7f59891e5419aa95e28f091133a8d12a4e

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 #2,285,073 on Chainz β†—
Circulating Supply:57,961,751 XPMΒ·at block #6,839,682 Β· updates every 60s
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