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Home/Chain Registry/Block #2,800,670

Block #2,800,670

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 8/19/2018, 11:44:53 AM Β· Difficulty 11.6714 Β· 4,039,662 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
758bbe83be13ea76d07511483cb9c67bae17dc37c56c07566acd053c91e2c4b1
View on Chainz β†—

Difficulty

11.671430

Transactions

1

Size

200 B

Version

2

Bits

0babe2d1

Nonce

1,774,855,470

Timestamp

8/19/2018, 11:44:53 AM

Confirmations

4,039,662

Merkle Root

b50712cba85cf1b80559896264051e385c18f2f044b78bdbd07cb43b817a8939
Transactions (1)
Coinbaseb50712cba85cf1…7cb43b817a8939
1 in β†’ 1 out7.3300 XPM110 B
ASwz2LxA…5teKPppE
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.

5.010 Γ— 10⁹⁡(96-digit number)
50109046934436402042…91203499273978260480
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
5.010 Γ— 10⁹⁡(96-digit number)
50109046934436402042…91203499273978260479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.010 Γ— 10⁹⁡(96-digit number)
50109046934436402042…91203499273978260481
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
1.002 Γ— 10⁹⁢(97-digit number)
10021809386887280408…82406998547956520959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.002 Γ— 10⁹⁢(97-digit number)
10021809386887280408…82406998547956520961
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
2.004 Γ— 10⁹⁢(97-digit number)
20043618773774560816…64813997095913041919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.004 Γ— 10⁹⁢(97-digit number)
20043618773774560816…64813997095913041921
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
4.008 Γ— 10⁹⁢(97-digit number)
40087237547549121633…29627994191826083839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.008 Γ— 10⁹⁢(97-digit number)
40087237547549121633…29627994191826083841
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
8.017 Γ— 10⁹⁢(97-digit number)
80174475095098243267…59255988383652167679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.017 Γ— 10⁹⁢(97-digit number)
80174475095098243267…59255988383652167681
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
1.603 Γ— 10⁹⁷(98-digit number)
16034895019019648653…18511976767304335359
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.603 Γ— 10⁹⁷(98-digit number)
16034895019019648653…18511976767304335361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2800670

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 758bbe83be13ea76d07511483cb9c67bae17dc37c56c07566acd053c91e2c4b1

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 #2,800,670 on Chainz β†—
Circulating Supply:57,966,976 XPMΒ·at block #6,840,331 Β· updates every 60s
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