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Home/Chain Registry/Block #2,683,933

Block #2,683,933

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/30/2018, 4:01:36 AM Β· Difficulty 11.6910 Β· 4,156,697 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
64100d75a393be566100dddf8554b1c13672adcb1830da643dfbec35d114089a
View on Chainz β†—

Difficulty

11.691027

Transactions

3

Size

619 B

Version

2

Bits

0bb0e720

Nonce

199,533,587

Timestamp

5/30/2018, 4:01:36 AM

Confirmations

4,156,697

Merkle Root

09e57f0af408af1f26b04b89459793166c8f2efd3fc6d88b664b47f418aa4937
Transactions (3)
Coinbase97dc850926283f…4049a23d74f42f
1 in β†’ 1 out7.3209 XPM110 B
AR51KgD5…6dfQU9WT
0eb61db1e87fd6…7e4ca1a75378d9
1 in β†’ 2 out1.1265 XPM227 B
AHM4Lkw2…NaayHpzTAdRyi4Ls…BbJJ6nGF
a6d0f3e13c86d5…107f0b7950917d
1 in β†’ 1 out5.0000 XPM192 B
AbW8AKqG…47YJwoPc
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.

5.414 Γ— 10⁹⁡(96-digit number)
54141522452260709350…74318791581449839520
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
5.414 Γ— 10⁹⁡(96-digit number)
54141522452260709350…74318791581449839519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.414 Γ— 10⁹⁡(96-digit number)
54141522452260709350…74318791581449839521
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
1.082 Γ— 10⁹⁢(97-digit number)
10828304490452141870…48637583162899679039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.082 Γ— 10⁹⁢(97-digit number)
10828304490452141870…48637583162899679041
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
2.165 Γ— 10⁹⁢(97-digit number)
21656608980904283740…97275166325799358079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.165 Γ— 10⁹⁢(97-digit number)
21656608980904283740…97275166325799358081
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
4.331 Γ— 10⁹⁢(97-digit number)
43313217961808567480…94550332651598716159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.331 Γ— 10⁹⁢(97-digit number)
43313217961808567480…94550332651598716161
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
8.662 Γ— 10⁹⁢(97-digit number)
86626435923617134961…89100665303197432319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.662 Γ— 10⁹⁢(97-digit number)
86626435923617134961…89100665303197432321
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
1.732 Γ— 10⁹⁷(98-digit number)
17325287184723426992…78201330606394864639
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 2683933

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 64100d75a393be566100dddf8554b1c13672adcb1830da643dfbec35d114089a

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 #2,683,933 on Chainz β†—
Circulating Supply:57,969,380 XPMΒ·at block #6,840,629 Β· updates every 60s
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