XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,867,366

Block #2,867,366

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/4/2018, 8:49:53 PM Β· Difficulty 11.6681 Β· 3,972,382 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
794b5ea6db8d1bfea66f6a8ae8aabf348f8c77512a4b21ad46d99cf9e7e667fc
View on Chainz β†—

Difficulty

11.668146

Transactions

1

Size

202 B

Version

2

Bits

0bab0b9c

Nonce

163,240,195

Timestamp

10/4/2018, 8:49:53 PM

Confirmations

3,972,382

Merkle Root

3d97f192e898cddf70a74da9ec1f561aefba92a165862c89b49b6b4a9df3f0a5
Transactions (1)
Coinbase3d97f192e898cd…9b6b4a9df3f0a5
1 in β†’ 1 out7.3300 XPM110 B
AXSrtYJh…fV8Dcmwr
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.

1.203 Γ— 10⁹⁹(100-digit number)
12037433305395391280…64701785823562301440
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
1.203 Γ— 10⁹⁹(100-digit number)
12037433305395391280…64701785823562301439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.203 Γ— 10⁹⁹(100-digit number)
12037433305395391280…64701785823562301441
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
2.407 Γ— 10⁹⁹(100-digit number)
24074866610790782560…29403571647124602879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.407 Γ— 10⁹⁹(100-digit number)
24074866610790782560…29403571647124602881
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
4.814 Γ— 10⁹⁹(100-digit number)
48149733221581565121…58807143294249205759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.814 Γ— 10⁹⁹(100-digit number)
48149733221581565121…58807143294249205761
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
9.629 Γ— 10⁹⁹(100-digit number)
96299466443163130243…17614286588498411519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.629 Γ— 10⁹⁹(100-digit number)
96299466443163130243…17614286588498411521
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
1.925 Γ— 10¹⁰⁰(101-digit number)
19259893288632626048…35228573176996823039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.925 Γ— 10¹⁰⁰(101-digit number)
19259893288632626048…35228573176996823041
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
3.851 Γ— 10¹⁰⁰(101-digit number)
38519786577265252097…70457146353993646079
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 2867366

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 794b5ea6db8d1bfea66f6a8ae8aabf348f8c77512a4b21ad46d99cf9e7e667fc

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 #2,867,366 on Chainz β†—
Circulating Supply:57,962,272 XPMΒ·at block #6,839,747 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