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Home/Chain Registry/Block #2,641,360

Block #2,641,360

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 7:55:47 AM Β· Difficulty 11.6176 Β· 4,198,171 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
074009d1f02c4c60dfdf6ac887e1ab915936431fdd0e2160af2205fe13daa02a
View on Chainz β†—

Difficulty

11.617619

Transactions

2

Size

393 B

Version

2

Bits

0b9e1c41

Nonce

1,590,372,061

Timestamp

5/1/2018, 7:55:47 AM

Confirmations

4,198,171

Merkle Root

f4d38a24099d8127987b1f17234ae572eed49a9aa4edb7d639d5e5d17d7bbbf5
Transactions (2)
Coinbase8cf8564dc3191c…a06c2ef3dae6e9
1 in β†’ 1 out7.4100 XPM110 B
Acy9s5ZR…VqGzwmis
f8d2e337598334…550f25cba3374e
1 in β†’ 2 out7.5700 XPM192 B
AGRwRCLk…i3H1nRMTATt8vVZX…8WgwsJUS
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.

4.648 Γ— 10⁹⁷(98-digit number)
46486923350249162591…74042077629032038400
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
4.648 Γ— 10⁹⁷(98-digit number)
46486923350249162591…74042077629032038399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.648 Γ— 10⁹⁷(98-digit number)
46486923350249162591…74042077629032038401
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
9.297 Γ— 10⁹⁷(98-digit number)
92973846700498325182…48084155258064076799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.297 Γ— 10⁹⁷(98-digit number)
92973846700498325182…48084155258064076801
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
1.859 Γ— 10⁹⁸(99-digit number)
18594769340099665036…96168310516128153599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.859 Γ— 10⁹⁸(99-digit number)
18594769340099665036…96168310516128153601
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
3.718 Γ— 10⁹⁸(99-digit number)
37189538680199330072…92336621032256307199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.718 Γ— 10⁹⁸(99-digit number)
37189538680199330072…92336621032256307201
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
7.437 Γ— 10⁹⁸(99-digit number)
74379077360398660145…84673242064512614399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.437 Γ— 10⁹⁸(99-digit number)
74379077360398660145…84673242064512614401
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
1.487 Γ— 10⁹⁹(100-digit number)
14875815472079732029…69346484129025228799
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 2641360

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 074009d1f02c4c60dfdf6ac887e1ab915936431fdd0e2160af2205fe13daa02a

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 #2,641,360 on Chainz β†—
Circulating Supply:57,960,538 XPMΒ·at block #6,839,530 Β· updates every 60s
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