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Home/Chain Registry/Block #2,932,200

Block #2,932,200

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/20/2018, 11:33:50 PM Β· Difficulty 11.4003 Β· 3,899,655 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e5576cd82fde32c6a14545471699c4bfda13ea0820815f6f8f6279111013c2e2
View on Chainz β†—

Difficulty

11.400313

Transactions

1

Size

200 B

Version

2

Bits

0b667af0

Nonce

732,586,172

Timestamp

11/20/2018, 11:33:50 PM

Confirmations

3,899,655

Merkle Root

591300754bb4efdc73f1d53f468dbcf5ca3ff0c8c6e135a722da398641a571bf
Transactions (1)
Coinbase591300754bb4ef…da398641a571bf
1 in β†’ 1 out7.6800 XPM110 B
AbXwmGxD…4XXYP765
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.

1.841 Γ— 10⁹⁴(95-digit number)
18418174058834475089…13800452821314837700
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
1.841 Γ— 10⁹⁴(95-digit number)
18418174058834475089…13800452821314837699
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.841 Γ— 10⁹⁴(95-digit number)
18418174058834475089…13800452821314837701
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
3.683 Γ— 10⁹⁴(95-digit number)
36836348117668950179…27600905642629675399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.683 Γ— 10⁹⁴(95-digit number)
36836348117668950179…27600905642629675401
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
7.367 Γ— 10⁹⁴(95-digit number)
73672696235337900358…55201811285259350799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.367 Γ— 10⁹⁴(95-digit number)
73672696235337900358…55201811285259350801
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
1.473 Γ— 10⁹⁡(96-digit number)
14734539247067580071…10403622570518701599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.473 Γ— 10⁹⁡(96-digit number)
14734539247067580071…10403622570518701601
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
2.946 Γ— 10⁹⁡(96-digit number)
29469078494135160143…20807245141037403199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.946 Γ— 10⁹⁡(96-digit number)
29469078494135160143…20807245141037403201
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
5.893 Γ— 10⁹⁡(96-digit number)
58938156988270320286…41614490282074806399
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 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
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 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 2932200

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 e5576cd82fde32c6a14545471699c4bfda13ea0820815f6f8f6279111013c2e2

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 #2,932,200 on Chainz β†—
Circulating Supply:57,898,961 XPMΒ·at block #6,831,854 Β· updates every 60s
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