XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,655,116

Block #2,655,116

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/9/2018, 10:03:56 PM Β· Difficulty 11.7103 Β· 4,181,288 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
75215132d57d7ac9b2b2fcb3e22258adb504d550fcedc84961e1c28f24d713c4
View on Chainz β†—

Difficulty

11.710281

Transactions

3

Size

2.22 KB

Version

2

Bits

0bb5d502

Nonce

1,438,978,924

Timestamp

5/9/2018, 10:03:56 PM

Confirmations

4,181,288

Merkle Root

a5d134594c70b697542ea0a301a013eadd4bd453c19b5b71c3976384acf5dc5a
Transactions (3)
Coinbase5e00c2923ceb00…d0720c66a43868
1 in β†’ 1 out7.3100 XPM110 B
Adqah8zh…1WwoHJ9t
8774f658698a99…3cda41d30c22f9
12 in β†’ 2 out42.8800 XPM1.81 KB
ALHcnV6E…JacbXs3EARbhkJP6…Ftyb5oMy
51083d7596b051…71866286bda0a2
1 in β†’ 2 out7.9800 XPM225 B
ASA6zLJZ…W2MdZiX1AZ4UnHzJ…PH7NQioA
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.

3.398 Γ— 10⁹⁡(96-digit number)
33983350547299914952…89428177156824340080
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
3.398 Γ— 10⁹⁡(96-digit number)
33983350547299914952…89428177156824340079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.398 Γ— 10⁹⁡(96-digit number)
33983350547299914952…89428177156824340081
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
6.796 Γ— 10⁹⁡(96-digit number)
67966701094599829905…78856354313648680159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.796 Γ— 10⁹⁡(96-digit number)
67966701094599829905…78856354313648680161
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
1.359 Γ— 10⁹⁢(97-digit number)
13593340218919965981…57712708627297360319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.359 Γ— 10⁹⁢(97-digit number)
13593340218919965981…57712708627297360321
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
2.718 Γ— 10⁹⁢(97-digit number)
27186680437839931962…15425417254594720639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.718 Γ— 10⁹⁢(97-digit number)
27186680437839931962…15425417254594720641
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
5.437 Γ— 10⁹⁢(97-digit number)
54373360875679863924…30850834509189441279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.437 Γ— 10⁹⁢(97-digit number)
54373360875679863924…30850834509189441281
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
1.087 Γ— 10⁹⁷(98-digit number)
10874672175135972784…61701669018378882559
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 2655116

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 75215132d57d7ac9b2b2fcb3e22258adb504d550fcedc84961e1c28f24d713c4

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 #2,655,116 on Chainz β†—
Circulating Supply:57,935,496 XPMΒ·at block #6,836,403 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy