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Home/Chain Registry/Block #2,778,726

Block #2,778,726

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/4/2018, 11:18:56 AM Β· Difficulty 11.6493 Β· 4,059,990 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ef827a0a675904b46b176837e061ff1764ca7bd40950dd874a5c337492d92093
View on Chainz β†—

Difficulty

11.649330

Transactions

2

Size

2.73 KB

Version

2

Bits

0ba63a7e

Nonce

1,778,277,620

Timestamp

8/4/2018, 11:18:56 AM

Confirmations

4,059,990

Merkle Root

ce1d665a9a5c72b0ceaf3312df152928a842468320c9ad44d8fabad0553108c8
Transactions (2)
Coinbased9818c88b8e8ff…e7c548f68c5dbc
1 in β†’ 1 out7.3900 XPM110 B
AUw14pmp…4m5NDrKT
41338d2a7d816a…3bdb654e14fa24
17 in β†’ 2 out10163.3442 XPM2.53 KB
AWktDgJA…jXBcWkfsAek4ofV3…M6GBS6AU
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.

3.619 Γ— 10⁹⁷(98-digit number)
36198310108474947692…78204803082275307520
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
3.619 Γ— 10⁹⁷(98-digit number)
36198310108474947692…78204803082275307519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.619 Γ— 10⁹⁷(98-digit number)
36198310108474947692…78204803082275307521
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
7.239 Γ— 10⁹⁷(98-digit number)
72396620216949895385…56409606164550615039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.239 Γ— 10⁹⁷(98-digit number)
72396620216949895385…56409606164550615041
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
1.447 Γ— 10⁹⁸(99-digit number)
14479324043389979077…12819212329101230079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.447 Γ— 10⁹⁸(99-digit number)
14479324043389979077…12819212329101230081
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
2.895 Γ— 10⁹⁸(99-digit number)
28958648086779958154…25638424658202460159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.895 Γ— 10⁹⁸(99-digit number)
28958648086779958154…25638424658202460161
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
5.791 Γ— 10⁹⁸(99-digit number)
57917296173559916308…51276849316404920319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.791 Γ— 10⁹⁸(99-digit number)
57917296173559916308…51276849316404920321
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
1.158 Γ— 10⁹⁹(100-digit number)
11583459234711983261…02553698632809840639
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 2778726

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 ef827a0a675904b46b176837e061ff1764ca7bd40950dd874a5c337492d92093

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 #2,778,726 on Chainz β†—
Circulating Supply:57,953,996 XPMΒ·at block #6,838,715 Β· updates every 60s
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