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Home/Chain Registry/Block #2,140,565

Block #2,140,565

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/1/2017, 2:21:36 PM Β· Difficulty 10.8756 Β· 4,701,974 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f2b5b7e9773215ee9a090ad6e02a6d591e47fc324c45c9475cb451ca98a6ba0b
View on Chainz β†—

Difficulty

10.875629

Transactions

1

Size

200 B

Version

2

Bits

0ae02937

Nonce

94,847,897

Timestamp

6/1/2017, 2:21:36 PM

Confirmations

4,701,974

Merkle Root

895782f25e1dc2e73ca3678fa8af22e2c49297b269bec92b4ffa3be44c9886d3
Transactions (1)
Coinbase895782f25e1dc2…fa3be44c9886d3
1 in β†’ 1 out8.4400 XPM109 B
AUiJHsdk…x3SED9ac
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.

2.831 Γ— 10⁹⁷(98-digit number)
28310848007701563992…10612951786577633280
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
2.831 Γ— 10⁹⁷(98-digit number)
28310848007701563992…10612951786577633279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.831 Γ— 10⁹⁷(98-digit number)
28310848007701563992…10612951786577633281
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
5.662 Γ— 10⁹⁷(98-digit number)
56621696015403127985…21225903573155266559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.662 Γ— 10⁹⁷(98-digit number)
56621696015403127985…21225903573155266561
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
1.132 Γ— 10⁹⁸(99-digit number)
11324339203080625597…42451807146310533119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.132 Γ— 10⁹⁸(99-digit number)
11324339203080625597…42451807146310533121
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
2.264 Γ— 10⁹⁸(99-digit number)
22648678406161251194…84903614292621066239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.264 Γ— 10⁹⁸(99-digit number)
22648678406161251194…84903614292621066241
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
4.529 Γ— 10⁹⁸(99-digit number)
45297356812322502388…69807228585242132479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.529 Γ— 10⁹⁸(99-digit number)
45297356812322502388…69807228585242132481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2140565

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 f2b5b7e9773215ee9a090ad6e02a6d591e47fc324c45c9475cb451ca98a6ba0b

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 #2,140,565 on Chainz β†—
Circulating Supply:57,984,735 XPMΒ·at block #6,842,538 Β· updates every 60s
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