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Block #2,812,802

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/27/2018, 9:36:25 PM Β· Difficulty 11.6732 Β· 4,020,550 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
87bbda37832f0b956fe8ee89d4d1b2246ffaba55680fd9c9ce9a4b84978efc4e
View on Chainz β†—

Difficulty

11.673173

Transactions

1

Size

201 B

Version

2

Bits

0bac550b

Nonce

461,672,332

Timestamp

8/27/2018, 9:36:25 PM

Confirmations

4,020,550

Merkle Root

6c0f3b114c65c6bb9aca17924fcb8386c24a8f1b09b5ecb59307227b87043b6b
Transactions (1)
Coinbase6c0f3b114c65c6…07227b87043b6b
1 in β†’ 1 out7.3300 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.

1.550 Γ— 10⁹⁢(97-digit number)
15501612658629737929…79574228861532979200
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
1.550 Γ— 10⁹⁢(97-digit number)
15501612658629737929…79574228861532979201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.100 Γ— 10⁹⁢(97-digit number)
31003225317259475859…59148457723065958401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.200 Γ— 10⁹⁢(97-digit number)
62006450634518951719…18296915446131916801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.240 Γ— 10⁹⁷(98-digit number)
12401290126903790343…36593830892263833601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.480 Γ— 10⁹⁷(98-digit number)
24802580253807580687…73187661784527667201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.960 Γ— 10⁹⁷(98-digit number)
49605160507615161375…46375323569055334401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.921 Γ— 10⁹⁷(98-digit number)
99210321015230322751…92750647138110668801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.984 Γ— 10⁹⁸(99-digit number)
19842064203046064550…85501294276221337601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.968 Γ— 10⁹⁸(99-digit number)
39684128406092129100…71002588552442675201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.936 Γ— 10⁹⁸(99-digit number)
79368256812184258201…42005177104885350401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.587 Γ— 10⁹⁹(100-digit number)
15873651362436851640…84010354209770700801
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 2812802

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 87bbda37832f0b956fe8ee89d4d1b2246ffaba55680fd9c9ce9a4b84978efc4e

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 #2,812,802 on Chainz β†—
Circulating Supply:57,911,014 XPMΒ·at block #6,833,351 Β· updates every 60s
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