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Home/Chain Registry/Block #2,134,796

Block #2,134,796

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/27/2017, 2:30:54 PM Β· Difficulty 10.9060 Β· 4,705,599 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b18718f923b81f95c4c4f9c079bbccee687ccfeab6856e2a37218e23568d890c
View on Chainz β†—

Difficulty

10.906024

Transactions

1

Size

199 B

Version

2

Bits

0ae7f12b

Nonce

1,657,819,679

Timestamp

5/27/2017, 2:30:54 PM

Confirmations

4,705,599

Merkle Root

9f074319320c97f6b204654c6ced2559914baa840a901015c74a6d23a20642a1
Transactions (1)
Coinbase9f074319320c97…4a6d23a20642a1
1 in β†’ 1 out8.3900 XPM109 B
AbRx41nv…Mw2nDyo6
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.

2.205 Γ— 10⁹⁡(96-digit number)
22051276151765058305…48886152703007396480
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
2.205 Γ— 10⁹⁡(96-digit number)
22051276151765058305…48886152703007396479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.205 Γ— 10⁹⁡(96-digit number)
22051276151765058305…48886152703007396481
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
4.410 Γ— 10⁹⁡(96-digit number)
44102552303530116610…97772305406014792959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.410 Γ— 10⁹⁡(96-digit number)
44102552303530116610…97772305406014792961
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
8.820 Γ— 10⁹⁡(96-digit number)
88205104607060233221…95544610812029585919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.820 Γ— 10⁹⁡(96-digit number)
88205104607060233221…95544610812029585921
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
1.764 Γ— 10⁹⁢(97-digit number)
17641020921412046644…91089221624059171839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.764 Γ— 10⁹⁢(97-digit number)
17641020921412046644…91089221624059171841
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
3.528 Γ— 10⁹⁢(97-digit number)
35282041842824093288…82178443248118343679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.528 Γ— 10⁹⁢(97-digit number)
35282041842824093288…82178443248118343681
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 2134796

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 b18718f923b81f95c4c4f9c079bbccee687ccfeab6856e2a37218e23568d890c

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 #2,134,796 on Chainz β†—
Circulating Supply:57,967,481 XPMΒ·at block #6,840,394 Β· updates every 60s
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