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Home/Chain Registry/Block #2,811,350

Block #2,811,350

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/26/2018, 10:56:23 PM Β· Difficulty 11.6671 Β· 4,030,763 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
596b66acc51095ddd833f1cf86c05a5511f1bc3f4e8d908d000a8a9bbefa15be
View on Chainz β†—

Difficulty

11.667121

Transactions

1

Size

201 B

Version

2

Bits

0baac871

Nonce

1,912,475,234

Timestamp

8/26/2018, 10:56:23 PM

Confirmations

4,030,763

Merkle Root

c8f6063d85fe00cc69e52d55f8678806c832817a2992ca88db0709ebfc15680a
Transactions (1)
Coinbasec8f6063d85fe00…0709ebfc15680a
1 in β†’ 1 out7.3300 XPM110 B
AMRvMdke…8FAQZN2d
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.

1.830 Γ— 10⁹⁷(98-digit number)
18300122060599681848…04101279950582087680
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
1.830 Γ— 10⁹⁷(98-digit number)
18300122060599681848…04101279950582087679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.830 Γ— 10⁹⁷(98-digit number)
18300122060599681848…04101279950582087681
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
3.660 Γ— 10⁹⁷(98-digit number)
36600244121199363697…08202559901164175359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.660 Γ— 10⁹⁷(98-digit number)
36600244121199363697…08202559901164175361
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
7.320 Γ— 10⁹⁷(98-digit number)
73200488242398727394…16405119802328350719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.320 Γ— 10⁹⁷(98-digit number)
73200488242398727394…16405119802328350721
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
1.464 Γ— 10⁹⁸(99-digit number)
14640097648479745478…32810239604656701439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.464 Γ— 10⁹⁸(99-digit number)
14640097648479745478…32810239604656701441
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
2.928 Γ— 10⁹⁸(99-digit number)
29280195296959490957…65620479209313402879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.928 Γ— 10⁹⁸(99-digit number)
29280195296959490957…65620479209313402881
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
5.856 Γ— 10⁹⁸(99-digit number)
58560390593918981915…31240958418626805759
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 2811350

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 596b66acc51095ddd833f1cf86c05a5511f1bc3f4e8d908d000a8a9bbefa15be

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 #2,811,350 on Chainz β†—
Circulating Supply:57,981,292 XPMΒ·at block #6,842,112 Β· updates every 60s
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