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Home/Chain Registry/Block #2,863,471

Block #2,863,471

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/2/2018, 2:11:13 AM Β· Difficulty 11.6747 Β· 3,979,561 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
27b989172129dc4622fe378749993cec2afc66f0fd61ace7dbd52de66e0d0c0e
View on Chainz β†—

Difficulty

11.674740

Transactions

1

Size

199 B

Version

2

Bits

0bacbbbe

Nonce

314,127,032

Timestamp

10/2/2018, 2:11:13 AM

Confirmations

3,979,561

Merkle Root

7f3e6c401e6e6657b95f468f73a893fc542110c7229cb9e84bb7751963e107b0
Transactions (1)
Coinbase7f3e6c401e6e66…b7751963e107b0
1 in β†’ 1 out7.3200 XPM110 B
AKM2JCz9…MZErdbX7
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.

5.850 Γ— 10⁹¹(92-digit number)
58505091343000636300…06402019296404694800
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
5.850 Γ— 10⁹¹(92-digit number)
58505091343000636300…06402019296404694801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.170 Γ— 10⁹²(93-digit number)
11701018268600127260…12804038592809389601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.340 Γ— 10⁹²(93-digit number)
23402036537200254520…25608077185618779201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.680 Γ— 10⁹²(93-digit number)
46804073074400509040…51216154371237558401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.360 Γ— 10⁹²(93-digit number)
93608146148801018080…02432308742475116801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.872 Γ— 10⁹³(94-digit number)
18721629229760203616…04864617484950233601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.744 Γ— 10⁹³(94-digit number)
37443258459520407232…09729234969900467201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.488 Γ— 10⁹³(94-digit number)
74886516919040814464…19458469939800934401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.497 Γ— 10⁹⁴(95-digit number)
14977303383808162892…38916939879601868801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.995 Γ— 10⁹⁴(95-digit number)
29954606767616325785…77833879759203737601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.990 Γ— 10⁹⁴(95-digit number)
59909213535232651571…55667759518407475201
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 2863471

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 27b989172129dc4622fe378749993cec2afc66f0fd61ace7dbd52de66e0d0c0e

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 #2,863,471 on Chainz β†—
Circulating Supply:57,988,611 XPMΒ·at block #6,843,031 Β· updates every 60s
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