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Home/Chain Registry/Block #2,838,106

Block #2,838,106

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2018, 11:16:53 PM Β· Difficulty 11.7177 Β· 4,004,253 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
da56d7e023cf3cd080d115f630252e06fa28d3c87e67b507a8c5b8acfec2f944
View on Chainz β†—

Difficulty

11.717703

Transactions

1

Size

202 B

Version

2

Bits

0bb7bb63

Nonce

821,878,296

Timestamp

9/13/2018, 11:16:53 PM

Confirmations

4,004,253

Merkle Root

2d855c7d77f2b37f17b25eae8973fda2378d5e364488ae8c06f210b78b26c776
Transactions (1)
Coinbase2d855c7d77f2b3…f210b78b26c776
1 in β†’ 1 out7.2700 XPM110 B
AZtxQr2F…7grUWrUz
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.

3.700 Γ— 10⁹⁸(99-digit number)
37000271930356163617…51163754454656614400
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
3.700 Γ— 10⁹⁸(99-digit number)
37000271930356163617…51163754454656614399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.700 Γ— 10⁹⁸(99-digit number)
37000271930356163617…51163754454656614401
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
7.400 Γ— 10⁹⁸(99-digit number)
74000543860712327235…02327508909313228799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.400 Γ— 10⁹⁸(99-digit number)
74000543860712327235…02327508909313228801
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
1.480 Γ— 10⁹⁹(100-digit number)
14800108772142465447…04655017818626457599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.480 Γ— 10⁹⁹(100-digit number)
14800108772142465447…04655017818626457601
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
2.960 Γ— 10⁹⁹(100-digit number)
29600217544284930894…09310035637252915199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.960 Γ— 10⁹⁹(100-digit number)
29600217544284930894…09310035637252915201
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
5.920 Γ— 10⁹⁹(100-digit number)
59200435088569861788…18620071274505830399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.920 Γ— 10⁹⁹(100-digit number)
59200435088569861788…18620071274505830401
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
1.184 Γ— 10¹⁰⁰(101-digit number)
11840087017713972357…37240142549011660799
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 2838106

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 da56d7e023cf3cd080d115f630252e06fa28d3c87e67b507a8c5b8acfec2f944

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 #2,838,106 on Chainz β†—
Circulating Supply:57,983,279 XPMΒ·at block #6,842,358 Β· updates every 60s
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