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Home/Chain Registry/Block #2,806,029

Block #2,806,029

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/23/2018, 5:19:17 AM Β· Difficulty 11.6706 Β· 4,035,640 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
92516247eceb12675bf51c28a6d5e86bded7d8855ad9d277f588654ea0a0ba84
View on Chainz β†—

Difficulty

11.670622

Transactions

1

Size

200 B

Version

2

Bits

0babade5

Nonce

567,155,202

Timestamp

8/23/2018, 5:19:17 AM

Confirmations

4,035,640

Merkle Root

3a19967156a9f3a1c7f302bd19dfc317ccc141b10cd8ddf1318ee3b4151edad9
Transactions (1)
Coinbase3a19967156a9f3…8ee3b4151edad9
1 in β†’ 1 out7.3300 XPM110 B
AYdG69Hb…qvRkMbyD
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.

4.737 Γ— 10⁹⁴(95-digit number)
47375657633002103587…13756227701479251360
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
4.737 Γ— 10⁹⁴(95-digit number)
47375657633002103587…13756227701479251359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.475 Γ— 10⁹⁴(95-digit number)
94751315266004207174…27512455402958502719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.895 Γ— 10⁹⁡(96-digit number)
18950263053200841434…55024910805917005439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.790 Γ— 10⁹⁡(96-digit number)
37900526106401682869…10049821611834010879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.580 Γ— 10⁹⁡(96-digit number)
75801052212803365739…20099643223668021759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.516 Γ— 10⁹⁢(97-digit number)
15160210442560673147…40199286447336043519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.032 Γ— 10⁹⁢(97-digit number)
30320420885121346295…80398572894672087039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.064 Γ— 10⁹⁢(97-digit number)
60640841770242692591…60797145789344174079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.212 Γ— 10⁹⁷(98-digit number)
12128168354048538518…21594291578688348159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.425 Γ— 10⁹⁷(98-digit number)
24256336708097077036…43188583157376696319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.851 Γ— 10⁹⁷(98-digit number)
48512673416194154073…86377166314753392639
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 2806029

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 92516247eceb12675bf51c28a6d5e86bded7d8855ad9d277f588654ea0a0ba84

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 #2,806,029 on Chainz β†—
Circulating Supply:57,977,742 XPMΒ·at block #6,841,668 Β· updates every 60s
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