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Home/Chain Registry/Block #2,177,922

Block #2,177,922

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/25/2017, 7:55:46 PM Β· Difficulty 10.9246 Β· 4,667,398 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4a978abaf5f665a676b465f55f2ea2183bd54a0c439de9f992f46cabd997e35a
View on Chainz β†—

Difficulty

10.924591

Transactions

1

Size

201 B

Version

2

Bits

0aecb1fc

Nonce

1,499,416,190

Timestamp

6/25/2017, 7:55:46 PM

Confirmations

4,667,398

Merkle Root

a1b9490ba32a395da6ff740957a9436276bf6aef941079e0d6827449ad936fc7
Transactions (1)
Coinbasea1b9490ba32a39…827449ad936fc7
1 in β†’ 1 out8.3700 XPM110 B
AVZZLmjT…Dr9dXw9i
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.

2.755 Γ— 10⁹⁢(97-digit number)
27555362516598441316…90353752835695608320
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
2.755 Γ— 10⁹⁢(97-digit number)
27555362516598441316…90353752835695608319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.755 Γ— 10⁹⁢(97-digit number)
27555362516598441316…90353752835695608321
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
5.511 Γ— 10⁹⁢(97-digit number)
55110725033196882633…80707505671391216639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.511 Γ— 10⁹⁢(97-digit number)
55110725033196882633…80707505671391216641
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
1.102 Γ— 10⁹⁷(98-digit number)
11022145006639376526…61415011342782433279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.102 Γ— 10⁹⁷(98-digit number)
11022145006639376526…61415011342782433281
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
2.204 Γ— 10⁹⁷(98-digit number)
22044290013278753053…22830022685564866559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.204 Γ— 10⁹⁷(98-digit number)
22044290013278753053…22830022685564866561
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
4.408 Γ— 10⁹⁷(98-digit number)
44088580026557506106…45660045371129733119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.408 Γ— 10⁹⁷(98-digit number)
44088580026557506106…45660045371129733121
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 2177922

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 4a978abaf5f665a676b465f55f2ea2183bd54a0c439de9f992f46cabd997e35a

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 #2,177,922 on Chainz β†—
Circulating Supply:58,006,999 XPMΒ·at block #6,845,319 Β· updates every 60s
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