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Home/Chain Registry/Block #2,775,140

Block #2,775,140

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/1/2018, 7:22:14 PM Β· Difficulty 11.6661 Β· 4,063,752 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
220db1ec5ad190ccc26c5d01ce67471ae9bbc8c8db108e78653d7fdc7f3822ad
View on Chainz β†—

Difficulty

11.666094

Transactions

1

Size

200 B

Version

2

Bits

0baa8525

Nonce

1,111,925,011

Timestamp

8/1/2018, 7:22:14 PM

Confirmations

4,063,752

Merkle Root

acc4d9af7ccdc1cb0fa3bf379b38ced27231b9977e6e28d3363630f5025d437e
Transactions (1)
Coinbaseacc4d9af7ccdc1…3630f5025d437e
1 in β†’ 1 out7.3400 XPM110 B
AcwfJtix…9SC9u3v8
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.

4.331 Γ— 10⁹⁡(96-digit number)
43317824114311260256…98984446137788707840
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
4.331 Γ— 10⁹⁡(96-digit number)
43317824114311260256…98984446137788707839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.331 Γ— 10⁹⁡(96-digit number)
43317824114311260256…98984446137788707841
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
8.663 Γ— 10⁹⁡(96-digit number)
86635648228622520512…97968892275577415679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.663 Γ— 10⁹⁡(96-digit number)
86635648228622520512…97968892275577415681
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
1.732 Γ— 10⁹⁢(97-digit number)
17327129645724504102…95937784551154831359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.732 Γ— 10⁹⁢(97-digit number)
17327129645724504102…95937784551154831361
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
3.465 Γ— 10⁹⁢(97-digit number)
34654259291449008204…91875569102309662719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.465 Γ— 10⁹⁢(97-digit number)
34654259291449008204…91875569102309662721
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
6.930 Γ— 10⁹⁢(97-digit number)
69308518582898016409…83751138204619325439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.930 Γ— 10⁹⁢(97-digit number)
69308518582898016409…83751138204619325441
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
1.386 Γ— 10⁹⁷(98-digit number)
13861703716579603281…67502276409238650879
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 2775140

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 220db1ec5ad190ccc26c5d01ce67471ae9bbc8c8db108e78653d7fdc7f3822ad

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 #2,775,140 on Chainz β†—
Circulating Supply:57,955,406 XPMΒ·at block #6,838,891 Β· updates every 60s
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