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Block #2,291,577

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/11/2017, 4:32:19 AM Β· Difficulty 10.9550 Β· 4,544,945 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3a7c710646e26279355b7db41e36a08a7d1e2ceca24384a98813c0d876d403ff
View on Chainz β†—

Difficulty

10.954990

Transactions

1

Size

198 B

Version

2

Bits

0af47a3c

Nonce

711,108,258

Timestamp

9/11/2017, 4:32:19 AM

Confirmations

4,544,945

Merkle Root

7e8302eaf9bf4a3de560c29e000de0c3c7115b55b1d491199915407d20e586c3
Transactions (1)
Coinbase7e8302eaf9bf4a…15407d20e586c3
1 in β†’ 1 out8.3200 XPM109 B
ASSKgYAD…un6NQY9q
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.

3.230 Γ— 10⁹²(93-digit number)
32307393243319503524…28353110714720011040
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
3.230 Γ— 10⁹²(93-digit number)
32307393243319503524…28353110714720011039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.230 Γ— 10⁹²(93-digit number)
32307393243319503524…28353110714720011041
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
6.461 Γ— 10⁹²(93-digit number)
64614786486639007049…56706221429440022079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.461 Γ— 10⁹²(93-digit number)
64614786486639007049…56706221429440022081
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
1.292 Γ— 10⁹³(94-digit number)
12922957297327801409…13412442858880044159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.292 Γ— 10⁹³(94-digit number)
12922957297327801409…13412442858880044161
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
2.584 Γ— 10⁹³(94-digit number)
25845914594655602819…26824885717760088319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.584 Γ— 10⁹³(94-digit number)
25845914594655602819…26824885717760088321
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
5.169 Γ— 10⁹³(94-digit number)
51691829189311205639…53649771435520176639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.169 Γ— 10⁹³(94-digit number)
51691829189311205639…53649771435520176641
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 2291577

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 3a7c710646e26279355b7db41e36a08a7d1e2ceca24384a98813c0d876d403ff

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 #2,291,577 on Chainz β†—
Circulating Supply:57,936,444 XPMΒ·at block #6,836,521 Β· updates every 60s
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