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Block #2,468,599

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/11/2018, 10:34:18 PM Β· Difficulty 10.9601 Β· 4,374,213 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
48e19ff84141faf7511e791740d8826ea89a33b26224ecd06cca80a973cfeaa8
View on Chainz β†—

Difficulty

10.960090

Transactions

1

Size

200 B

Version

2

Bits

0af5c86d

Nonce

640,947,707

Timestamp

1/11/2018, 10:34:18 PM

Confirmations

4,374,213

Merkle Root

24e8939e8558bb7249146d567cf68e383f98ec491fe354724ff0ecb973705a8a
Transactions (1)
Coinbase24e8939e8558bb…f0ecb973705a8a
1 in β†’ 1 out8.3100 XPM110 B
APSwRzD5…Z8wf3LNL
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.

3.447 Γ— 10⁹⁴(95-digit number)
34472174129570359186…57319763385129282880
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
3.447 Γ— 10⁹⁴(95-digit number)
34472174129570359186…57319763385129282879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.447 Γ— 10⁹⁴(95-digit number)
34472174129570359186…57319763385129282881
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
6.894 Γ— 10⁹⁴(95-digit number)
68944348259140718373…14639526770258565759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.894 Γ— 10⁹⁴(95-digit number)
68944348259140718373…14639526770258565761
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
1.378 Γ— 10⁹⁡(96-digit number)
13788869651828143674…29279053540517131519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.378 Γ— 10⁹⁡(96-digit number)
13788869651828143674…29279053540517131521
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
2.757 Γ— 10⁹⁡(96-digit number)
27577739303656287349…58558107081034263039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.757 Γ— 10⁹⁡(96-digit number)
27577739303656287349…58558107081034263041
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
5.515 Γ— 10⁹⁡(96-digit number)
55155478607312574698…17116214162068526079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.515 Γ— 10⁹⁡(96-digit number)
55155478607312574698…17116214162068526081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2468599

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 48e19ff84141faf7511e791740d8826ea89a33b26224ecd06cca80a973cfeaa8

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 #2,468,599 on Chainz β†—
Circulating Supply:57,986,836 XPMΒ·at block #6,842,811 Β· updates every 60s
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