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Home/Chain Registry/Block #2,880,592

Block #2,880,592

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 10/14/2018, 9:51:17 AM Β· Difficulty 11.6329 Β· 3,956,314 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
db52278218a6951a04683213d158e8aa98b21c96bbc3a5148abf4c5fb5e19e5a
View on Chainz β†—

Difficulty

11.632903

Transactions

1

Size

200 B

Version

2

Bits

0ba205f1

Nonce

1,130,259,241

Timestamp

10/14/2018, 9:51:17 AM

Confirmations

3,956,314

Merkle Root

c0c9d042d54f70d2d057b2243f5a17bf1c3ce4f348dc2d8c30d7f6eb58f1993e
Transactions (1)
Coinbasec0c9d042d54f70…d7f6eb58f1993e
1 in β†’ 1 out7.3800 XPM110 B
AKggj6tX…behprVZR
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.

1.925 Γ— 10⁹⁡(96-digit number)
19259545573077178349…27987982612124264100
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
1.925 Γ— 10⁹⁡(96-digit number)
19259545573077178349…27987982612124264099
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.925 Γ— 10⁹⁡(96-digit number)
19259545573077178349…27987982612124264101
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
3.851 Γ— 10⁹⁡(96-digit number)
38519091146154356699…55975965224248528199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.851 Γ— 10⁹⁡(96-digit number)
38519091146154356699…55975965224248528201
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
7.703 Γ— 10⁹⁡(96-digit number)
77038182292308713398…11951930448497056399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.703 Γ— 10⁹⁡(96-digit number)
77038182292308713398…11951930448497056401
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
1.540 Γ— 10⁹⁢(97-digit number)
15407636458461742679…23903860896994112799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.540 Γ— 10⁹⁢(97-digit number)
15407636458461742679…23903860896994112801
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
3.081 Γ— 10⁹⁢(97-digit number)
30815272916923485359…47807721793988225599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.081 Γ— 10⁹⁢(97-digit number)
30815272916923485359…47807721793988225601
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
6.163 Γ— 10⁹⁢(97-digit number)
61630545833846970718…95615443587976451199
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
6.163 Γ— 10⁹⁢(97-digit number)
61630545833846970718…95615443587976451201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2880592

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 db52278218a6951a04683213d158e8aa98b21c96bbc3a5148abf4c5fb5e19e5a

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 #2,880,592 on Chainz β†—
Circulating Supply:57,939,541 XPMΒ·at block #6,836,905 Β· updates every 60s
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