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Home/Chain Registry/Block #2,866,298

Block #2,866,298

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/4/2018, 3:10:54 AM Β· Difficulty 11.6677 Β· 3,966,442 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d78808cf6f9637affa25b0cf7130b59359bd21943c14a27fc0427eec1d4dda1f
View on Chainz β†—

Difficulty

11.667682

Transactions

1

Size

199 B

Version

2

Bits

0baaed36

Nonce

1,327,658,833

Timestamp

10/4/2018, 3:10:54 AM

Confirmations

3,966,442

Merkle Root

20c22028f706f251c6036a22beeb0b9464d39542a3831e659c7f53ce389df1c2
Transactions (1)
Coinbase20c22028f706f2…7f53ce389df1c2
1 in β†’ 1 out7.3300 XPM109 B
AN15tDTB…w8MfS7pG
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.

8.885 Γ— 10⁹³(94-digit number)
88859361496619183135…07511265913253857080
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
8.885 Γ— 10⁹³(94-digit number)
88859361496619183135…07511265913253857079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.777 Γ— 10⁹⁴(95-digit number)
17771872299323836627…15022531826507714159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.554 Γ— 10⁹⁴(95-digit number)
35543744598647673254…30045063653015428319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.108 Γ— 10⁹⁴(95-digit number)
71087489197295346508…60090127306030856639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.421 Γ— 10⁹⁡(96-digit number)
14217497839459069301…20180254612061713279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.843 Γ— 10⁹⁡(96-digit number)
28434995678918138603…40360509224123426559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.686 Γ— 10⁹⁡(96-digit number)
56869991357836277206…80721018448246853119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.137 Γ— 10⁹⁢(97-digit number)
11373998271567255441…61442036896493706239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.274 Γ— 10⁹⁢(97-digit number)
22747996543134510882…22884073792987412479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.549 Γ— 10⁹⁢(97-digit number)
45495993086269021765…45768147585974824959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.099 Γ— 10⁹⁢(97-digit number)
90991986172538043530…91536295171949649919
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 2866298

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 d78808cf6f9637affa25b0cf7130b59359bd21943c14a27fc0427eec1d4dda1f

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 #2,866,298 on Chainz β†—
Circulating Supply:57,906,079 XPMΒ·at block #6,832,739 Β· updates every 60s
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