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Home/Chain Registry/Block #2,641,730

Block #2,641,730

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 11:28:46 AM Β· Difficulty 11.6294 Β· 4,192,026 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a649fdbbe55cf748828989e65abab9dcc67112e1750f58b57ddc9380dfc79f50
View on Chainz β†—

Difficulty

11.629405

Transactions

1

Size

202 B

Version

2

Bits

0ba120aa

Nonce

332,125,365

Timestamp

5/1/2018, 11:28:46 AM

Confirmations

4,192,026

Merkle Root

ee71c3225cb50ca68a7e3a3428a3b291e91471a67d9affad1d08327b0cc049af
Transactions (1)
Coinbaseee71c3225cb50c…08327b0cc049af
1 in β†’ 1 out7.3800 XPM110 B
Adqah8zh…1WwoHJ9t
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.

3.475 Γ— 10⁹⁸(99-digit number)
34752966583514032114…26550371599231549440
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
3.475 Γ— 10⁹⁸(99-digit number)
34752966583514032114…26550371599231549439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.475 Γ— 10⁹⁸(99-digit number)
34752966583514032114…26550371599231549441
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
6.950 Γ— 10⁹⁸(99-digit number)
69505933167028064229…53100743198463098879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.950 Γ— 10⁹⁸(99-digit number)
69505933167028064229…53100743198463098881
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
1.390 Γ— 10⁹⁹(100-digit number)
13901186633405612845…06201486396926197759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.390 Γ— 10⁹⁹(100-digit number)
13901186633405612845…06201486396926197761
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
2.780 Γ— 10⁹⁹(100-digit number)
27802373266811225691…12402972793852395519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.780 Γ— 10⁹⁹(100-digit number)
27802373266811225691…12402972793852395521
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
5.560 Γ— 10⁹⁹(100-digit number)
55604746533622451383…24805945587704791039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.560 Γ— 10⁹⁹(100-digit number)
55604746533622451383…24805945587704791041
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
1.112 Γ— 10¹⁰⁰(101-digit number)
11120949306724490276…49611891175409582079
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 2641730

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 a649fdbbe55cf748828989e65abab9dcc67112e1750f58b57ddc9380dfc79f50

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 #2,641,730 on Chainz β†—
Circulating Supply:57,914,265 XPMΒ·at block #6,833,755 Β· updates every 60s
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