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Home/Chain Registry/Block #2,836,023

Block #2,836,023

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 9/12/2018, 1:14:26 PM Β· Difficulty 11.7153 Β· 4,006,313 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d19ead9e8a3c63a8a94b1607d8184fdee65fea635317ce04ee1159a25c8ca223
View on Chainz β†—

Difficulty

11.715348

Transactions

2

Size

1.14 KB

Version

2

Bits

0bb72114

Nonce

73,122,724

Timestamp

9/12/2018, 1:14:26 PM

Confirmations

4,006,313

Merkle Root

a6948894930506535c152f16f107144ace00c531651756ce2ea0723faa1cd746
Transactions (2)
Coinbasef22417cf1dca16…93de23243f65fb
1 in β†’ 1 out7.2800 XPM110 B
APzHyWy2…iUrJHDs9
843542700c555f…0128cf82066deb
6 in β†’ 2 out1.0187 XPM967 B
AaxCraKt…CEBafb4NAJd7z5iR…JrCM18MN
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.

9.438 Γ— 10⁹³(94-digit number)
94386495194285653701…26701026876543692200
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
9.438 Γ— 10⁹³(94-digit number)
94386495194285653701…26701026876543692199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.438 Γ— 10⁹³(94-digit number)
94386495194285653701…26701026876543692201
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
1.887 Γ— 10⁹⁴(95-digit number)
18877299038857130740…53402053753087384399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.887 Γ— 10⁹⁴(95-digit number)
18877299038857130740…53402053753087384401
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
3.775 Γ— 10⁹⁴(95-digit number)
37754598077714261480…06804107506174768799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.775 Γ— 10⁹⁴(95-digit number)
37754598077714261480…06804107506174768801
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
7.550 Γ— 10⁹⁴(95-digit number)
75509196155428522961…13608215012349537599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.550 Γ— 10⁹⁴(95-digit number)
75509196155428522961…13608215012349537601
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
1.510 Γ— 10⁹⁡(96-digit number)
15101839231085704592…27216430024699075199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.510 Γ— 10⁹⁡(96-digit number)
15101839231085704592…27216430024699075201
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
3.020 Γ— 10⁹⁡(96-digit number)
30203678462171409184…54432860049398150399
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
3.020 Γ— 10⁹⁡(96-digit number)
30203678462171409184…54432860049398150401
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 2836023

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 d19ead9e8a3c63a8a94b1607d8184fdee65fea635317ce04ee1159a25c8ca223

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 #2,836,023 on Chainz β†—
Circulating Supply:57,983,094 XPMΒ·at block #6,842,335 Β· updates every 60s
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