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Block #2,640,507

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 12:51:38 AM Β· Difficulty 11.5837 Β· 4,201,721 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
32352840ed1d9ca78ed45bba767924253bb75bcd3fd4d75fbe906ccea8adf6fe
View on Chainz β†—

Difficulty

11.583678

Transactions

1

Size

200 B

Version

2

Bits

0b956be4

Nonce

98,151,851

Timestamp

5/1/2018, 12:51:38 AM

Confirmations

4,201,721

Merkle Root

bd26f46621e00eb1f7a2bbdeb23a216ede7549f5d147a158c2079970738c53f3
Transactions (1)
Coinbasebd26f46621e00e…079970738c53f3
1 in β†’ 1 out7.4400 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.

1.072 Γ— 10⁹⁡(96-digit number)
10722193255578581977…13936997942240126400
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
1.072 Γ— 10⁹⁡(96-digit number)
10722193255578581977…13936997942240126399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.072 Γ— 10⁹⁡(96-digit number)
10722193255578581977…13936997942240126401
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
2.144 Γ— 10⁹⁡(96-digit number)
21444386511157163954…27873995884480252799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.144 Γ— 10⁹⁡(96-digit number)
21444386511157163954…27873995884480252801
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
4.288 Γ— 10⁹⁡(96-digit number)
42888773022314327909…55747991768960505599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.288 Γ— 10⁹⁡(96-digit number)
42888773022314327909…55747991768960505601
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
8.577 Γ— 10⁹⁡(96-digit number)
85777546044628655818…11495983537921011199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.577 Γ— 10⁹⁡(96-digit number)
85777546044628655818…11495983537921011201
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
1.715 Γ— 10⁹⁢(97-digit number)
17155509208925731163…22991967075842022399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.715 Γ— 10⁹⁢(97-digit number)
17155509208925731163…22991967075842022401
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
3.431 Γ— 10⁹⁢(97-digit number)
34311018417851462327…45983934151684044799
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 2640507

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 32352840ed1d9ca78ed45bba767924253bb75bcd3fd4d75fbe906ccea8adf6fe

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 #2,640,507 on Chainz β†—
Circulating Supply:57,982,223 XPMΒ·at block #6,842,227 Β· updates every 60s
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