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Home/Chain Registry/Block #2,819,563

Block #2,819,563

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/1/2018, 6:48:49 AM Β· Difficulty 11.7013 Β· 4,014,457 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d1ccb71ac279599388f3e066e157184f3e28e5151c85e06c5a8a70e2971abcd5
View on Chainz β†—

Difficulty

11.701304

Transactions

1

Size

202 B

Version

2

Bits

0bb388a6

Nonce

1,187,250,174

Timestamp

9/1/2018, 6:48:49 AM

Confirmations

4,014,457

Merkle Root

c0a0c6d32e2411a84cd7aa613f96be3d7051657afbe52fb6a963b48b0f937447
Transactions (1)
Coinbasec0a0c6d32e2411…63b48b0f937447
1 in β†’ 1 out7.2900 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.

4.384 Γ— 10⁹⁸(99-digit number)
43842899992990735092…28082143839126896640
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
4.384 Γ— 10⁹⁸(99-digit number)
43842899992990735092…28082143839126896639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.384 Γ— 10⁹⁸(99-digit number)
43842899992990735092…28082143839126896641
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
8.768 Γ— 10⁹⁸(99-digit number)
87685799985981470184…56164287678253793279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.768 Γ— 10⁹⁸(99-digit number)
87685799985981470184…56164287678253793281
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
1.753 Γ— 10⁹⁹(100-digit number)
17537159997196294036…12328575356507586559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.753 Γ— 10⁹⁹(100-digit number)
17537159997196294036…12328575356507586561
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
3.507 Γ— 10⁹⁹(100-digit number)
35074319994392588073…24657150713015173119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.507 Γ— 10⁹⁹(100-digit number)
35074319994392588073…24657150713015173121
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
7.014 Γ— 10⁹⁹(100-digit number)
70148639988785176147…49314301426030346239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.014 Γ— 10⁹⁹(100-digit number)
70148639988785176147…49314301426030346241
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
1.402 Γ— 10¹⁰⁰(101-digit number)
14029727997757035229…98628602852060692479
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 2819563

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 d1ccb71ac279599388f3e066e157184f3e28e5151c85e06c5a8a70e2971abcd5

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 #2,819,563 on Chainz β†—
Circulating Supply:57,916,385 XPMΒ·at block #6,834,019 Β· updates every 60s
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