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Block #2,802,312

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2018, 3:12:19 PM Β· Difficulty 11.6711 Β· 4,040,502 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c889252742c456bac23c0d8d827f646ed8ecd3c0e5ef8034f089e32f9ed3e477
View on Chainz β†—

Difficulty

11.671117

Transactions

1

Size

200 B

Version

2

Bits

0babce4b

Nonce

696,195,430

Timestamp

8/20/2018, 3:12:19 PM

Confirmations

4,040,502

Merkle Root

73f1852dbad2a6fe989460b5ed70bd743179bd92430f0edefb9bcaf97f434482
Transactions (1)
Coinbase73f1852dbad2a6…9bcaf97f434482
1 in β†’ 1 out7.3300 XPM109 B
ANK1V8kp…DQAzvUGk
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.

1.482 Γ— 10⁹⁸(99-digit number)
14828946390963091807…91947011343144468480
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.482 Γ— 10⁹⁸(99-digit number)
14828946390963091807…91947011343144468481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.965 Γ— 10⁹⁸(99-digit number)
29657892781926183614…83894022686288936961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.931 Γ— 10⁹⁸(99-digit number)
59315785563852367229…67788045372577873921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.186 Γ— 10⁹⁹(100-digit number)
11863157112770473445…35576090745155747841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.372 Γ— 10⁹⁹(100-digit number)
23726314225540946891…71152181490311495681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.745 Γ— 10⁹⁹(100-digit number)
47452628451081893783…42304362980622991361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.490 Γ— 10⁹⁹(100-digit number)
94905256902163787567…84608725961245982721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.898 Γ— 10¹⁰⁰(101-digit number)
18981051380432757513…69217451922491965441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.796 Γ— 10¹⁰⁰(101-digit number)
37962102760865515026…38434903844983930881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.592 Γ— 10¹⁰⁰(101-digit number)
75924205521731030053…76869807689967861761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.518 Γ— 10¹⁰¹(102-digit number)
15184841104346206010…53739615379935723521
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2802312

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 c889252742c456bac23c0d8d827f646ed8ecd3c0e5ef8034f089e32f9ed3e477

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 #2,802,312 on Chainz β†—
Circulating Supply:57,986,852 XPMΒ·at block #6,842,813 Β· updates every 60s
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