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Home/Chain Registry/Block #2,650,365

Block #2,650,365

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/5/2018, 11:57:36 PM Β· Difficulty 11.7572 Β· 4,190,459 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e9ac422e13cf979d9d859228c978f3a5e4bbc23c2733f79c1f3ce818819331e5
View on Chainz β†—

Difficulty

11.757186

Transactions

1

Size

202 B

Version

2

Bits

0bc1d6ef

Nonce

1,033,484,201

Timestamp

5/5/2018, 11:57:36 PM

Confirmations

4,190,459

Merkle Root

9209109cb1b7136afd7e64e21a89011e65173f38e3d0893145f98bcf2d5d3076
Transactions (1)
Coinbase9209109cb1b713…f98bcf2d5d3076
1 in β†’ 1 out7.2200 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.

3.152 Γ— 10⁹⁸(99-digit number)
31525630744224517694…35580768858085785600
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
3.152 Γ— 10⁹⁸(99-digit number)
31525630744224517694…35580768858085785599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.152 Γ— 10⁹⁸(99-digit number)
31525630744224517694…35580768858085785601
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
6.305 Γ— 10⁹⁸(99-digit number)
63051261488449035389…71161537716171571199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.305 Γ— 10⁹⁸(99-digit number)
63051261488449035389…71161537716171571201
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
1.261 Γ— 10⁹⁹(100-digit number)
12610252297689807077…42323075432343142399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.261 Γ— 10⁹⁹(100-digit number)
12610252297689807077…42323075432343142401
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
2.522 Γ— 10⁹⁹(100-digit number)
25220504595379614155…84646150864686284799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.522 Γ— 10⁹⁹(100-digit number)
25220504595379614155…84646150864686284801
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
5.044 Γ— 10⁹⁹(100-digit number)
50441009190759228311…69292301729372569599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.044 Γ— 10⁹⁹(100-digit number)
50441009190759228311…69292301729372569601
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
1.008 Γ— 10¹⁰⁰(101-digit number)
10088201838151845662…38584603458745139199
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 2650365

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 e9ac422e13cf979d9d859228c978f3a5e4bbc23c2733f79c1f3ce818819331e5

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 #2,650,365 on Chainz β†—
Circulating Supply:57,970,945 XPMΒ·at block #6,840,823 Β· updates every 60s
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