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Home/Chain Registry/Block #2,726,214

Block #2,726,214

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/29/2018, 5:24:04 AM Β· Difficulty 11.6245 Β· 4,106,412 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a55be78feab7fa44c757dcbeb7a3e9485bdf151ba5aa1c99cc33a4437e359b04
View on Chainz β†—

Difficulty

11.624537

Transactions

2

Size

577 B

Version

2

Bits

0b9fe1b0

Nonce

434,291,026

Timestamp

6/29/2018, 5:24:04 AM

Confirmations

4,106,412

Merkle Root

d2f2ff42abe1e83b897a5029f4d9009d26affc39a4f647a9fb5c5860ef50c96b
Transactions (2)
Coinbase52ee772dfa627e…88abdf7621a700
1 in β†’ 1 out7.4000 XPM110 B
AZSqEooj…7pn3NzY7
da93429c70f8d8…2f9e47a30e159e
2 in β†’ 2 out200.0101 XPM376 B
AQmjqzoU…5U6sbve9ALZGnzQn…t19swE3v
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.

8.558 Γ— 10⁹⁷(98-digit number)
85580667107520641185…13737993552742318080
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
8.558 Γ— 10⁹⁷(98-digit number)
85580667107520641185…13737993552742318079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.558 Γ— 10⁹⁷(98-digit number)
85580667107520641185…13737993552742318081
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
1.711 Γ— 10⁹⁸(99-digit number)
17116133421504128237…27475987105484636159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.711 Γ— 10⁹⁸(99-digit number)
17116133421504128237…27475987105484636161
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
3.423 Γ— 10⁹⁸(99-digit number)
34232266843008256474…54951974210969272319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.423 Γ— 10⁹⁸(99-digit number)
34232266843008256474…54951974210969272321
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
6.846 Γ— 10⁹⁸(99-digit number)
68464533686016512948…09903948421938544639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.846 Γ— 10⁹⁸(99-digit number)
68464533686016512948…09903948421938544641
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
1.369 Γ— 10⁹⁹(100-digit number)
13692906737203302589…19807896843877089279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.369 Γ— 10⁹⁹(100-digit number)
13692906737203302589…19807896843877089281
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
2.738 Γ— 10⁹⁹(100-digit number)
27385813474406605179…39615793687754178559
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 2726214

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 a55be78feab7fa44c757dcbeb7a3e9485bdf151ba5aa1c99cc33a4437e359b04

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 #2,726,214 on Chainz β†—
Circulating Supply:57,905,156 XPMΒ·at block #6,832,625 Β· updates every 60s
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