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Home/Chain Registry/Block #2,833,411

Block #2,833,411

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 5:31:04 PM Β· Difficulty 11.7159 Β· 4,007,457 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
bb4c831bbd066458a68cdeec0e107f16ac1ef1a7278575127d93409a1e94cb02
View on Chainz β†—

Difficulty

11.715918

Transactions

1

Size

200 B

Version

2

Bits

0bb7466e

Nonce

624,230,917

Timestamp

9/10/2018, 5:31:04 PM

Confirmations

4,007,457

Merkle Root

0702fc4ccc77f95e81ccc02824d80ebcf5fd521b87a9d27c2f677f72a8330305
Transactions (1)
Coinbase0702fc4ccc77f9…677f72a8330305
1 in β†’ 1 out7.2700 XPM110 B
AZTJ7SCu…V2RuPRRT
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.

1.543 Γ— 10⁹⁴(95-digit number)
15430740647215875388…89855069610831459840
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.543 Γ— 10⁹⁴(95-digit number)
15430740647215875388…89855069610831459839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.543 Γ— 10⁹⁴(95-digit number)
15430740647215875388…89855069610831459841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.086 Γ— 10⁹⁴(95-digit number)
30861481294431750777…79710139221662919679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.086 Γ— 10⁹⁴(95-digit number)
30861481294431750777…79710139221662919681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
6.172 Γ— 10⁹⁴(95-digit number)
61722962588863501554…59420278443325839359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.172 Γ— 10⁹⁴(95-digit number)
61722962588863501554…59420278443325839361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.234 Γ— 10⁹⁡(96-digit number)
12344592517772700310…18840556886651678719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.234 Γ— 10⁹⁡(96-digit number)
12344592517772700310…18840556886651678721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.468 Γ— 10⁹⁡(96-digit number)
24689185035545400621…37681113773303357439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.468 Γ— 10⁹⁡(96-digit number)
24689185035545400621…37681113773303357441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.937 Γ— 10⁹⁡(96-digit number)
49378370071090801243…75362227546606714879
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
4.937 Γ— 10⁹⁡(96-digit number)
49378370071090801243…75362227546606714881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. 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
ExceptionalChain length 12
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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 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 2833411

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 bb4c831bbd066458a68cdeec0e107f16ac1ef1a7278575127d93409a1e94cb02

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 #2,833,411 on Chainz β†—
Circulating Supply:57,971,293 XPMΒ·at block #6,840,867 Β· updates every 60s
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