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Home/Chain Registry/Block #2,110,041

Block #2,110,041

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/10/2017, 12:45:47 PM Β· Difficulty 10.9020 Β· 4,728,333 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f2222f9a006cd7fff7c6c1e7eff0cea36a25539db8e2d7c91e27a9a0ec158106
View on Chainz β†—

Difficulty

10.901965

Transactions

1

Size

200 B

Version

2

Bits

0ae6e727

Nonce

948,919,470

Timestamp

5/10/2017, 12:45:47 PM

Confirmations

4,728,333

Merkle Root

d633e6768f4f02727a6b8077668057af7041444912a15e3b66709c174372fdfb
Transactions (1)
Coinbased633e6768f4f02…709c174372fdfb
1 in β†’ 1 out8.4000 XPM110 B
ARgJGDtW…1C4Z98ER
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.

1.680 Γ— 10⁹⁡(96-digit number)
16801466347972634027…67128678266286982400
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
1.680 Γ— 10⁹⁡(96-digit number)
16801466347972634027…67128678266286982399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.680 Γ— 10⁹⁡(96-digit number)
16801466347972634027…67128678266286982401
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
3.360 Γ— 10⁹⁡(96-digit number)
33602932695945268054…34257356532573964799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.360 Γ— 10⁹⁡(96-digit number)
33602932695945268054…34257356532573964801
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
6.720 Γ— 10⁹⁡(96-digit number)
67205865391890536108…68514713065147929599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.720 Γ— 10⁹⁡(96-digit number)
67205865391890536108…68514713065147929601
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
1.344 Γ— 10⁹⁢(97-digit number)
13441173078378107221…37029426130295859199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.344 Γ— 10⁹⁢(97-digit number)
13441173078378107221…37029426130295859201
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
2.688 Γ— 10⁹⁢(97-digit number)
26882346156756214443…74058852260591718399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.688 Γ— 10⁹⁢(97-digit number)
26882346156756214443…74058852260591718401
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
5.376 Γ— 10⁹⁢(97-digit number)
53764692313512428886…48117704521183436799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2110041

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 f2222f9a006cd7fff7c6c1e7eff0cea36a25539db8e2d7c91e27a9a0ec158106

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 #2,110,041 on Chainz β†—
Circulating Supply:57,951,262 XPMΒ·at block #6,838,373 Β· updates every 60s
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