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Home/Chain Registry/Block #2,784,887

Block #2,784,887

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/8/2018, 1:16:20 PM Β· Difficulty 11.6688 Β· 4,042,159 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7e3e44c37347f910aae53f191235de692cedf77f28cd8fe92126b3291fa055c0
View on Chainz β†—

Difficulty

11.668804

Transactions

1

Size

200 B

Version

2

Bits

0bab36b7

Nonce

258,932,004

Timestamp

8/8/2018, 1:16:20 PM

Confirmations

4,042,159

Merkle Root

4a713aa50e267c03b420c4cbabf0d5fa57978164dea4e5a85b3140ccdabc87d2
Transactions (1)
Coinbase4a713aa50e267c…3140ccdabc87d2
1 in β†’ 1 out7.3300 XPM110 B
AZwYFEmS…1kkvTHji
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.

8.466 Γ— 10⁹⁡(96-digit number)
84663404922422920078…89335701705263503840
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
8.466 Γ— 10⁹⁡(96-digit number)
84663404922422920078…89335701705263503839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.466 Γ— 10⁹⁡(96-digit number)
84663404922422920078…89335701705263503841
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
1.693 Γ— 10⁹⁢(97-digit number)
16932680984484584015…78671403410527007679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.693 Γ— 10⁹⁢(97-digit number)
16932680984484584015…78671403410527007681
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
3.386 Γ— 10⁹⁢(97-digit number)
33865361968969168031…57342806821054015359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.386 Γ— 10⁹⁢(97-digit number)
33865361968969168031…57342806821054015361
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
6.773 Γ— 10⁹⁢(97-digit number)
67730723937938336062…14685613642108030719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.773 Γ— 10⁹⁢(97-digit number)
67730723937938336062…14685613642108030721
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
1.354 Γ— 10⁹⁷(98-digit number)
13546144787587667212…29371227284216061439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.354 Γ— 10⁹⁷(98-digit number)
13546144787587667212…29371227284216061441
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
2.709 Γ— 10⁹⁷(98-digit number)
27092289575175334425…58742454568432122879
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 2784887

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 7e3e44c37347f910aae53f191235de692cedf77f28cd8fe92126b3291fa055c0

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 #2,784,887 on Chainz β†—
Circulating Supply:57,860,549 XPMΒ·at block #6,827,045 Β· updates every 60s
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