XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,684,872

Block #2,684,872

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 5/30/2018, 7:35:54 PM Β· Difficulty 11.6912 Β· 4,155,077 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fac664331a8b2526434d33a502209e897cbfe3951daa44b91368420fd401543b
View on Chainz β†—

Difficulty

11.691205

Transactions

1

Size

200 B

Version

2

Bits

0bb0f2c8

Nonce

552,110,031

Timestamp

5/30/2018, 7:35:54 PM

Confirmations

4,155,077

Merkle Root

7233e2fb3e29889e5522dd7505dd8fe4d728dd1ac4617add51d90319a2def28b
Transactions (1)
Coinbase7233e2fb3e2988…d90319a2def28b
1 in β†’ 1 out7.3000 XPM110 B
APVXsyvZ…Scn3FKYu
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.

8.859 Γ— 10⁹⁴(95-digit number)
88591759904390272855…39717833349881466880
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
8.859 Γ— 10⁹⁴(95-digit number)
88591759904390272855…39717833349881466879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.859 Γ— 10⁹⁴(95-digit number)
88591759904390272855…39717833349881466881
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
1.771 Γ— 10⁹⁡(96-digit number)
17718351980878054571…79435666699762933759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.771 Γ— 10⁹⁡(96-digit number)
17718351980878054571…79435666699762933761
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
3.543 Γ— 10⁹⁡(96-digit number)
35436703961756109142…58871333399525867519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.543 Γ— 10⁹⁡(96-digit number)
35436703961756109142…58871333399525867521
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
7.087 Γ— 10⁹⁡(96-digit number)
70873407923512218284…17742666799051735039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.087 Γ— 10⁹⁡(96-digit number)
70873407923512218284…17742666799051735041
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
1.417 Γ— 10⁹⁢(97-digit number)
14174681584702443656…35485333598103470079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.417 Γ— 10⁹⁢(97-digit number)
14174681584702443656…35485333598103470081
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
2.834 Γ— 10⁹⁢(97-digit number)
28349363169404887313…70970667196206940159
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
2.834 Γ— 10⁹⁢(97-digit number)
28349363169404887313…70970667196206940161
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 2684872

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 fac664331a8b2526434d33a502209e897cbfe3951daa44b91368420fd401543b

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 #2,684,872 on Chainz β†—
Circulating Supply:57,963,893 XPMΒ·at block #6,839,948 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