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Home/Chain Registry/Block #2,180,342

Block #2,180,342

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/27/2017, 3:58:51 AM Β· Difficulty 10.9317 Β· 4,663,240 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4f2b75f0e519470996719a3e5d04db69fc97f0af8874982e2485d571a1d9855d
View on Chainz β†—

Difficulty

10.931744

Transactions

1

Size

199 B

Version

2

Bits

0aee86c5

Nonce

489,399,430

Timestamp

6/27/2017, 3:58:51 AM

Confirmations

4,663,240

Merkle Root

492d0a7406b91427770332d2eee2ac2c981d72fce57d8f2279e06b51affcdc72
Transactions (1)
Coinbase492d0a7406b914…e06b51affcdc72
1 in β†’ 1 out8.3500 XPM109 B
ASFrdmF8…GBGwNiC6
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.

3.478 Γ— 10⁹⁴(95-digit number)
34785507904670469737…66781034589147913600
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
3.478 Γ— 10⁹⁴(95-digit number)
34785507904670469737…66781034589147913599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.478 Γ— 10⁹⁴(95-digit number)
34785507904670469737…66781034589147913601
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
6.957 Γ— 10⁹⁴(95-digit number)
69571015809340939474…33562069178295827199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.957 Γ— 10⁹⁴(95-digit number)
69571015809340939474…33562069178295827201
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
1.391 Γ— 10⁹⁡(96-digit number)
13914203161868187894…67124138356591654399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.391 Γ— 10⁹⁡(96-digit number)
13914203161868187894…67124138356591654401
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
2.782 Γ— 10⁹⁡(96-digit number)
27828406323736375789…34248276713183308799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.782 Γ— 10⁹⁡(96-digit number)
27828406323736375789…34248276713183308801
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
5.565 Γ— 10⁹⁡(96-digit number)
55656812647472751579…68496553426366617599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.565 Γ— 10⁹⁡(96-digit number)
55656812647472751579…68496553426366617601
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 2180342

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 4f2b75f0e519470996719a3e5d04db69fc97f0af8874982e2485d571a1d9855d

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 #2,180,342 on Chainz β†—
Circulating Supply:57,993,019 XPMΒ·at block #6,843,581 Β· updates every 60s
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