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Home/Chain Registry/Block #2,457,382

Block #2,457,382

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/4/2018, 2:40:00 PM Β· Difficulty 10.9541 Β· 4,386,646 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6dd017de92ac1bfd2f6bafe1815214caf1c3376fa58776d0cc1514c73bcfbd82
View on Chainz β†—

Difficulty

10.954124

Transactions

1

Size

200 B

Version

2

Bits

0af44179

Nonce

281,185,028

Timestamp

1/4/2018, 2:40:00 PM

Confirmations

4,386,646

Merkle Root

260360c21efa0d70ff7efe75c28a9d90648c3bb860e8e1bd116efdf7510b6521
Transactions (1)
Coinbase260360c21efa0d…6efdf7510b6521
1 in β†’ 1 out8.3200 XPM110 B
AMaC7Vtp…9xqNHBmG
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.

4.438 Γ— 10⁹⁴(95-digit number)
44380990073225662124…41016009249407508640
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
4.438 Γ— 10⁹⁴(95-digit number)
44380990073225662124…41016009249407508639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.438 Γ— 10⁹⁴(95-digit number)
44380990073225662124…41016009249407508641
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
8.876 Γ— 10⁹⁴(95-digit number)
88761980146451324249…82032018498815017279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.876 Γ— 10⁹⁴(95-digit number)
88761980146451324249…82032018498815017281
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
1.775 Γ— 10⁹⁡(96-digit number)
17752396029290264849…64064036997630034559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.775 Γ— 10⁹⁡(96-digit number)
17752396029290264849…64064036997630034561
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
3.550 Γ— 10⁹⁡(96-digit number)
35504792058580529699…28128073995260069119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.550 Γ— 10⁹⁡(96-digit number)
35504792058580529699…28128073995260069121
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
7.100 Γ— 10⁹⁡(96-digit number)
71009584117161059399…56256147990520138239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.100 Γ— 10⁹⁡(96-digit number)
71009584117161059399…56256147990520138241
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 2457382

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 6dd017de92ac1bfd2f6bafe1815214caf1c3376fa58776d0cc1514c73bcfbd82

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 #2,457,382 on Chainz β†—
Circulating Supply:57,996,601 XPMΒ·at block #6,844,027 Β· updates every 60s
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