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Home/Chain Registry/Block #2,684,213

Block #2,684,213

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/30/2018, 8:38:37 AM Β· Difficulty 11.6911 Β· 4,155,495 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
66ab961ec550569229983d6f63242a0472d4ad79c540a2b83b0be14519fb26ce
View on Chainz β†—

Difficulty

11.691121

Transactions

2

Size

1.14 KB

Version

2

Bits

0bb0ed4f

Nonce

737,809,656

Timestamp

5/30/2018, 8:38:37 AM

Confirmations

4,155,495

Merkle Root

0235e8e78e85ff7d7e761b83480e7cdde314a9641555a0685efd7cd931e9f69f
Transactions (2)
Coinbase1e4fd869501420…7a70c2f78e0169
1 in β†’ 1 out7.3200 XPM110 B
AMMXs1oV…GpxqLENE
540c201c7704f2…063cacf5cb8777
6 in β†’ 2 out3000.0100 XPM966 B
AeMYC4MS…V6GeDFsRAH3A2GJU…NLYdkucb
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.

1.153 Γ— 10⁹⁴(95-digit number)
11536807462659196179…44495877698017617680
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
1.153 Γ— 10⁹⁴(95-digit number)
11536807462659196179…44495877698017617679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.153 Γ— 10⁹⁴(95-digit number)
11536807462659196179…44495877698017617681
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
2.307 Γ— 10⁹⁴(95-digit number)
23073614925318392359…88991755396035235359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.307 Γ— 10⁹⁴(95-digit number)
23073614925318392359…88991755396035235361
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
4.614 Γ— 10⁹⁴(95-digit number)
46147229850636784719…77983510792070470719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.614 Γ— 10⁹⁴(95-digit number)
46147229850636784719…77983510792070470721
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
9.229 Γ— 10⁹⁴(95-digit number)
92294459701273569439…55967021584140941439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.229 Γ— 10⁹⁴(95-digit number)
92294459701273569439…55967021584140941441
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
1.845 Γ— 10⁹⁡(96-digit number)
18458891940254713887…11934043168281882879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.845 Γ— 10⁹⁡(96-digit number)
18458891940254713887…11934043168281882881
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
3.691 Γ— 10⁹⁡(96-digit number)
36917783880509427775…23868086336563765759
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 2684213

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 66ab961ec550569229983d6f63242a0472d4ad79c540a2b83b0be14519fb26ce

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 #2,684,213 on Chainz β†—
Circulating Supply:57,961,954 XPMΒ·at block #6,839,707 Β· updates every 60s
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