XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,838,105

Block #2,838,105

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 9/13/2018, 11:16:32 PM Β· Difficulty 11.7177 Β· 4,006,970 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9ebb4608806a874d50c11391bb7973063614d8bef1d0d8184cfc87bd3f0bf20d
View on Chainz β†—

Difficulty

11.717724

Transactions

1

Size

200 B

Version

2

Bits

0bb7bcbb

Nonce

700,412,537

Timestamp

9/13/2018, 11:16:32 PM

Confirmations

4,006,970

Merkle Root

641c73b3ce6e1237052aab8278ef103f12feca52f3bf753ec76540f5a93820e6
Transactions (1)
Coinbase641c73b3ce6e12…6540f5a93820e6
1 in β†’ 1 out7.2700 XPM110 B
AM9ywwMF…oF2LckRN
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.

1.230 Γ— 10⁹⁴(95-digit number)
12307551471773808189…48337634486292583920
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
1.230 Γ— 10⁹⁴(95-digit number)
12307551471773808189…48337634486292583919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.230 Γ— 10⁹⁴(95-digit number)
12307551471773808189…48337634486292583921
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
2.461 Γ— 10⁹⁴(95-digit number)
24615102943547616378…96675268972585167839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.461 Γ— 10⁹⁴(95-digit number)
24615102943547616378…96675268972585167841
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
4.923 Γ— 10⁹⁴(95-digit number)
49230205887095232757…93350537945170335679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.923 Γ— 10⁹⁴(95-digit number)
49230205887095232757…93350537945170335681
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
9.846 Γ— 10⁹⁴(95-digit number)
98460411774190465514…86701075890340671359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.846 Γ— 10⁹⁴(95-digit number)
98460411774190465514…86701075890340671361
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
1.969 Γ— 10⁹⁡(96-digit number)
19692082354838093102…73402151780681342719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.969 Γ— 10⁹⁡(96-digit number)
19692082354838093102…73402151780681342721
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
3.938 Γ— 10⁹⁡(96-digit number)
39384164709676186205…46804303561362685439
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
3.938 Γ— 10⁹⁡(96-digit number)
39384164709676186205…46804303561362685441
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 2838105

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 9ebb4608806a874d50c11391bb7973063614d8bef1d0d8184cfc87bd3f0bf20d

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 #2,838,105 on Chainz β†—
Circulating Supply:58,005,026 XPMΒ·at block #6,845,074 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