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Home/Chain Registry/Block #1,678,405

Block #1,678,405

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2016, 12:25:58 PM Β· Difficulty 10.6929 Β· 5,164,069 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
98c7dc38890d22f20f20d8c23b270b525ccb963eab1f5a06e188405e86541c51
View on Chainz β†—

Difficulty

10.692901

Transactions

1

Size

199 B

Version

2

Bits

0ab161fb

Nonce

426,755,918

Timestamp

7/18/2016, 12:25:58 PM

Confirmations

5,164,069

Merkle Root

5d3234c9adeabce1d8ca1a8d71d83c07e0ad5a58299532687f4106cd74b1838b
Transactions (1)
Coinbase5d3234c9adeabc…4106cd74b1838b
1 in β†’ 1 out8.7300 XPM109 B
AQTwLDfG…wASazSdv
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.

2.367 Γ— 10⁹⁴(95-digit number)
23677094727718206167…68919468825608529600
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
2.367 Γ— 10⁹⁴(95-digit number)
23677094727718206167…68919468825608529599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.367 Γ— 10⁹⁴(95-digit number)
23677094727718206167…68919468825608529601
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
4.735 Γ— 10⁹⁴(95-digit number)
47354189455436412334…37838937651217059199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.735 Γ— 10⁹⁴(95-digit number)
47354189455436412334…37838937651217059201
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
9.470 Γ— 10⁹⁴(95-digit number)
94708378910872824668…75677875302434118399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.470 Γ— 10⁹⁴(95-digit number)
94708378910872824668…75677875302434118401
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
1.894 Γ— 10⁹⁡(96-digit number)
18941675782174564933…51355750604868236799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.894 Γ— 10⁹⁡(96-digit number)
18941675782174564933…51355750604868236801
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
3.788 Γ— 10⁹⁡(96-digit number)
37883351564349129867…02711501209736473599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.788 Γ— 10⁹⁡(96-digit number)
37883351564349129867…02711501209736473601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1678405

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 98c7dc38890d22f20f20d8c23b270b525ccb963eab1f5a06e188405e86541c51

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 #1,678,405 on Chainz β†—
Circulating Supply:57,984,209 XPMΒ·at block #6,842,473 Β· updates every 60s
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