XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,662,121

Block #2,662,121

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/15/2018, 1:08:27 PM Β· Difficulty 11.6398 Β· 4,180,070 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
edfafa481f83f0a2dfaa75f3805b5b8acd0ecb5b56a350e8ef7cf035d26dd7a2
View on Chainz β†—

Difficulty

11.639795

Transactions

1

Size

199 B

Version

2

Bits

0ba3c99f

Nonce

898,198,545

Timestamp

5/15/2018, 1:08:27 PM

Confirmations

4,180,070

Merkle Root

c134463ba825341fdab5942cba9f5990ac63ec096326b1a3df4087a7904394e8
Transactions (1)
Coinbasec134463ba82534…4087a7904394e8
1 in β†’ 1 out7.3700 XPM110 B
ASjNvW1M…cppPtUB3
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.

3.015 Γ— 10⁹³(94-digit number)
30157477601495192847…79032771831512423390
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
3.015 Γ— 10⁹³(94-digit number)
30157477601495192847…79032771831512423389
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.015 Γ— 10⁹³(94-digit number)
30157477601495192847…79032771831512423391
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
6.031 Γ— 10⁹³(94-digit number)
60314955202990385695…58065543663024846779
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.031 Γ— 10⁹³(94-digit number)
60314955202990385695…58065543663024846781
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
1.206 Γ— 10⁹⁴(95-digit number)
12062991040598077139…16131087326049693559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.206 Γ— 10⁹⁴(95-digit number)
12062991040598077139…16131087326049693561
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
2.412 Γ— 10⁹⁴(95-digit number)
24125982081196154278…32262174652099387119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.412 Γ— 10⁹⁴(95-digit number)
24125982081196154278…32262174652099387121
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
4.825 Γ— 10⁹⁴(95-digit number)
48251964162392308556…64524349304198774239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.825 Γ— 10⁹⁴(95-digit number)
48251964162392308556…64524349304198774241
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
9.650 Γ— 10⁹⁴(95-digit number)
96503928324784617112…29048698608397548479
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 2662121

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 edfafa481f83f0a2dfaa75f3805b5b8acd0ecb5b56a350e8ef7cf035d26dd7a2

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 #2,662,121 on Chainz β†—
Circulating Supply:57,981,921 XPMΒ·at block #6,842,190 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