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Home/Chain Registry/Block #2,147,106

Block #2,147,106

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/5/2017, 3:15:07 PM Β· Difficulty 10.8925 Β· 4,693,292 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
be40b8dd89c0c4175a6a1ca13a8a385e9d65b9551342d54c4da21cc89842f03b
View on Chainz β†—

Difficulty

10.892526

Transactions

1

Size

201 B

Version

2

Bits

0ae47c91

Nonce

1,335,711,513

Timestamp

6/5/2017, 3:15:07 PM

Confirmations

4,693,292

Merkle Root

596ae654cd89b46c5b9c09d5a56aa057a54219e96ce964c7b0ac9d255bb7f68c
Transactions (1)
Coinbase596ae654cd89b4…ac9d255bb7f68c
1 in β†’ 1 out8.4100 XPM109 B
AHTeyvUm…BfQ4hiui
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.

3.506 Γ— 10⁹⁸(99-digit number)
35068552226330072899…59074726586835271680
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
3.506 Γ— 10⁹⁸(99-digit number)
35068552226330072899…59074726586835271679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.506 Γ— 10⁹⁸(99-digit number)
35068552226330072899…59074726586835271681
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
7.013 Γ— 10⁹⁸(99-digit number)
70137104452660145799…18149453173670543359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.013 Γ— 10⁹⁸(99-digit number)
70137104452660145799…18149453173670543361
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
1.402 Γ— 10⁹⁹(100-digit number)
14027420890532029159…36298906347341086719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.402 Γ— 10⁹⁹(100-digit number)
14027420890532029159…36298906347341086721
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
2.805 Γ— 10⁹⁹(100-digit number)
28054841781064058319…72597812694682173439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.805 Γ— 10⁹⁹(100-digit number)
28054841781064058319…72597812694682173441
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
5.610 Γ— 10⁹⁹(100-digit number)
56109683562128116639…45195625389364346879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.610 Γ— 10⁹⁹(100-digit number)
56109683562128116639…45195625389364346881
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 2147106

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 be40b8dd89c0c4175a6a1ca13a8a385e9d65b9551342d54c4da21cc89842f03b

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 #2,147,106 on Chainz β†—
Circulating Supply:57,967,506 XPMΒ·at block #6,840,397 Β· updates every 60s
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