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Home/Chain Registry/Block #2,819,105

Block #2,819,105

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/31/2018, 11:07:43 PM Β· Difficulty 11.7014 Β· 4,025,832 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d79cd00e368260f9667846839688f382dbc170084f5f12457f58e677cdee391c
View on Chainz β†—

Difficulty

11.701399

Transactions

1

Size

200 B

Version

2

Bits

0bb38ee1

Nonce

993,884,078

Timestamp

8/31/2018, 11:07:43 PM

Confirmations

4,025,832

Merkle Root

dd6a5d7baa313475c9d5e1a62c35dc1d92d176841f7f7897431a7edf087bbbed
Transactions (1)
Coinbasedd6a5d7baa3134…1a7edf087bbbed
1 in β†’ 1 out7.2900 XPM110 B
AKQwfzit…8aRJyyhh
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.

5.305 Γ— 10⁹³(94-digit number)
53057948318178753819…97404329564168079360
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
5.305 Γ— 10⁹³(94-digit number)
53057948318178753819…97404329564168079359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.305 Γ— 10⁹³(94-digit number)
53057948318178753819…97404329564168079361
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
1.061 Γ— 10⁹⁴(95-digit number)
10611589663635750763…94808659128336158719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.061 Γ— 10⁹⁴(95-digit number)
10611589663635750763…94808659128336158721
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
2.122 Γ— 10⁹⁴(95-digit number)
21223179327271501527…89617318256672317439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.122 Γ— 10⁹⁴(95-digit number)
21223179327271501527…89617318256672317441
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
4.244 Γ— 10⁹⁴(95-digit number)
42446358654543003055…79234636513344634879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.244 Γ— 10⁹⁴(95-digit number)
42446358654543003055…79234636513344634881
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
8.489 Γ— 10⁹⁴(95-digit number)
84892717309086006110…58469273026689269759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.489 Γ— 10⁹⁴(95-digit number)
84892717309086006110…58469273026689269761
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
1.697 Γ— 10⁹⁡(96-digit number)
16978543461817201222…16938546053378539519
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 2819105

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 d79cd00e368260f9667846839688f382dbc170084f5f12457f58e677cdee391c

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 #2,819,105 on Chainz β†—
Circulating Supply:58,003,914 XPMΒ·at block #6,844,936 Β· updates every 60s
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