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Home/Chain Registry/Block #3,002,673

Block #3,002,673

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/9/2019, 10:31:42 PM Β· Difficulty 11.2024 Β· 3,839,697 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4e849f7a5756bf28aa3e73012863071d02d462c1daff19051c9e2443d6690431
View on Chainz β†—

Difficulty

11.202364

Transactions

1

Size

200 B

Version

2

Bits

0b33ce24

Nonce

680,339,967

Timestamp

1/9/2019, 10:31:42 PM

Confirmations

3,839,697

Merkle Root

a8d9337dfd707164066a0350829448136908045368a3c766a05d7cd88f4f2b0f
Transactions (1)
Coinbasea8d9337dfd7071…5d7cd88f4f2b0f
1 in β†’ 1 out7.9600 XPM110 B
AbXwmGxD…4XXYP765
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.

8.657 Γ— 10⁹⁴(95-digit number)
86573415055128629287…24868823917133190400
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
8.657 Γ— 10⁹⁴(95-digit number)
86573415055128629287…24868823917133190399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.657 Γ— 10⁹⁴(95-digit number)
86573415055128629287…24868823917133190401
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
1.731 Γ— 10⁹⁡(96-digit number)
17314683011025725857…49737647834266380799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.731 Γ— 10⁹⁡(96-digit number)
17314683011025725857…49737647834266380801
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
3.462 Γ— 10⁹⁡(96-digit number)
34629366022051451714…99475295668532761599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.462 Γ— 10⁹⁡(96-digit number)
34629366022051451714…99475295668532761601
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
6.925 Γ— 10⁹⁡(96-digit number)
69258732044102903429…98950591337065523199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.925 Γ— 10⁹⁡(96-digit number)
69258732044102903429…98950591337065523201
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
1.385 Γ— 10⁹⁢(97-digit number)
13851746408820580685…97901182674131046399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.385 Γ— 10⁹⁢(97-digit number)
13851746408820580685…97901182674131046401
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
2.770 Γ— 10⁹⁢(97-digit number)
27703492817641161371…95802365348262092799
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 3002673

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 4e849f7a5756bf28aa3e73012863071d02d462c1daff19051c9e2443d6690431

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 #3,002,673 on Chainz β†—
Circulating Supply:57,983,370 XPMΒ·at block #6,842,369 Β· updates every 60s
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