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Block #2,111,524

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/11/2017, 12:41:30 PM Β· Difficulty 10.9029 Β· 4,734,124 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f30ad62f59f521cf672d487d3e3770cf433f02d589931b32a1cd22f401c26630
View on Chainz β†—

Difficulty

10.902924

Transactions

1

Size

200 B

Version

2

Bits

0ae72600

Nonce

409,398,336

Timestamp

5/11/2017, 12:41:30 PM

Confirmations

4,734,124

Merkle Root

d373da90b6dca0c4a138ecd471ffaeb01ca823aea3259dcfa1a80c4fecd1e222
Transactions (1)
Coinbased373da90b6dca0…a80c4fecd1e222
1 in β†’ 1 out8.4000 XPM110 B
ALJKgPat…eXiFvs2i
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.

5.774 Γ— 10⁹³(94-digit number)
57747776453149397856…27169585294964971680
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
5.774 Γ— 10⁹³(94-digit number)
57747776453149397856…27169585294964971679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.774 Γ— 10⁹³(94-digit number)
57747776453149397856…27169585294964971681
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
1.154 Γ— 10⁹⁴(95-digit number)
11549555290629879571…54339170589929943359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.154 Γ— 10⁹⁴(95-digit number)
11549555290629879571…54339170589929943361
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
2.309 Γ— 10⁹⁴(95-digit number)
23099110581259759142…08678341179859886719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.309 Γ— 10⁹⁴(95-digit number)
23099110581259759142…08678341179859886721
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
4.619 Γ— 10⁹⁴(95-digit number)
46198221162519518285…17356682359719773439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.619 Γ— 10⁹⁴(95-digit number)
46198221162519518285…17356682359719773441
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
9.239 Γ— 10⁹⁴(95-digit number)
92396442325039036570…34713364719439546879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.239 Γ— 10⁹⁴(95-digit number)
92396442325039036570…34713364719439546881
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 2111524

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 f30ad62f59f521cf672d487d3e3770cf433f02d589931b32a1cd22f401c26630

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 #2,111,524 on Chainz β†—
Circulating Supply:58,009,633 XPMΒ·at block #6,845,647 Β· updates every 60s
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