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Home/Chain Registry/Block #2,391,250

Block #2,391,250

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/23/2017, 3:58:09 AM Β· Difficulty 10.8728 Β· 4,450,631 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ddfc96ef55e6069d44785298655bd1bd9478402c949d8e87f4956d0bdb37f3bf
View on Chainz β†—

Difficulty

10.872844

Transactions

2

Size

425 B

Version

2

Bits

0adf72b6

Nonce

137,113,862

Timestamp

11/23/2017, 3:58:09 AM

Confirmations

4,450,631

Merkle Root

706ad9b67bdb17a5128bc0d04654a89e923a1873a228e9d025cff474a0d7f9f8
Transactions (2)
Coinbase25f1992b82aae9…6ea97502d7f49b
1 in β†’ 1 out8.4600 XPM109 B
AbLvtdnu…PorvQuHh
0c57c71a7386c2…69d83118426627
1 in β†’ 2 out4.4219 XPM226 B
AaaYoKho…cUUmc4TjASaEhpP5…P6LguCM3
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.

8.245 Γ— 10⁹⁴(95-digit number)
82450319323901956846…53077159937755494400
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
8.245 Γ— 10⁹⁴(95-digit number)
82450319323901956846…53077159937755494399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.245 Γ— 10⁹⁴(95-digit number)
82450319323901956846…53077159937755494401
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
1.649 Γ— 10⁹⁡(96-digit number)
16490063864780391369…06154319875510988799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.649 Γ— 10⁹⁡(96-digit number)
16490063864780391369…06154319875510988801
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
3.298 Γ— 10⁹⁡(96-digit number)
32980127729560782738…12308639751021977599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.298 Γ— 10⁹⁡(96-digit number)
32980127729560782738…12308639751021977601
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
6.596 Γ— 10⁹⁡(96-digit number)
65960255459121565477…24617279502043955199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.596 Γ— 10⁹⁡(96-digit number)
65960255459121565477…24617279502043955201
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
1.319 Γ— 10⁹⁢(97-digit number)
13192051091824313095…49234559004087910399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.319 Γ— 10⁹⁢(97-digit number)
13192051091824313095…49234559004087910401
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 2391250

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 ddfc96ef55e6069d44785298655bd1bd9478402c949d8e87f4956d0bdb37f3bf

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 #2,391,250 on Chainz β†—
Circulating Supply:57,979,423 XPMΒ·at block #6,841,880 Β· updates every 60s
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