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Home/Chain Registry/Block #2,178,196

Block #2,178,196

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/25/2017, 11:44:15 PM Β· Difficulty 10.9253 Β· 4,665,818 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9c2dbe947320a1c8568026aacdb1fc42b06edb1ab088a4c01b23167b88ef07fd
View on Chainz β†—

Difficulty

10.925265

Transactions

1

Size

201 B

Version

2

Bits

0aecde33

Nonce

494,317,222

Timestamp

6/25/2017, 11:44:15 PM

Confirmations

4,665,818

Merkle Root

d8610b96415a37886da3e98f127c93da4bf3225dd8656cb06ef384b7cde198f2
Transactions (1)
Coinbased8610b96415a37…f384b7cde198f2
1 in β†’ 1 out8.3600 XPM110 B
AJHag3Hg…sC57Vd9i
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.

1.289 Γ— 10⁹⁷(98-digit number)
12897423002759221564…70288121000939530240
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
1.289 Γ— 10⁹⁷(98-digit number)
12897423002759221564…70288121000939530239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.289 Γ— 10⁹⁷(98-digit number)
12897423002759221564…70288121000939530241
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
2.579 Γ— 10⁹⁷(98-digit number)
25794846005518443129…40576242001879060479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.579 Γ— 10⁹⁷(98-digit number)
25794846005518443129…40576242001879060481
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
5.158 Γ— 10⁹⁷(98-digit number)
51589692011036886259…81152484003758120959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.158 Γ— 10⁹⁷(98-digit number)
51589692011036886259…81152484003758120961
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
1.031 Γ— 10⁹⁸(99-digit number)
10317938402207377251…62304968007516241919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.031 Γ— 10⁹⁸(99-digit number)
10317938402207377251…62304968007516241921
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
2.063 Γ— 10⁹⁸(99-digit number)
20635876804414754503…24609936015032483839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.063 Γ— 10⁹⁸(99-digit number)
20635876804414754503…24609936015032483841
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 2178196

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 9c2dbe947320a1c8568026aacdb1fc42b06edb1ab088a4c01b23167b88ef07fd

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 #2,178,196 on Chainz β†—
Circulating Supply:57,996,495 XPMΒ·at block #6,844,013 Β· updates every 60s
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