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Home/Chain Registry/Block #2,643,269

Block #2,643,269

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 1:16:44 AM Β· Difficulty 11.6782 Β· 4,187,718 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
446e90069d133f017ee548c62d141e06e5074646c46b833c569eb10a90a14c64
View on Chainz β†—

Difficulty

11.678248

Transactions

1

Size

200 B

Version

2

Bits

0bada1ac

Nonce

144,532,623

Timestamp

5/2/2018, 1:16:44 AM

Confirmations

4,187,718

Merkle Root

11d9b8c717724dd4120f18203e6cd81f450ac247d0367922a571df07c3da2157
Transactions (1)
Coinbase11d9b8c717724d…71df07c3da2157
1 in β†’ 1 out7.3200 XPM110 B
AdEabeJd…Q9p5vb1V
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.

5.556 Γ— 10⁹³(94-digit number)
55569381210147088352…64734847293182962240
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
5.556 Γ— 10⁹³(94-digit number)
55569381210147088352…64734847293182962239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.556 Γ— 10⁹³(94-digit number)
55569381210147088352…64734847293182962241
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
1.111 Γ— 10⁹⁴(95-digit number)
11113876242029417670…29469694586365924479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.111 Γ— 10⁹⁴(95-digit number)
11113876242029417670…29469694586365924481
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
2.222 Γ— 10⁹⁴(95-digit number)
22227752484058835341…58939389172731848959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.222 Γ— 10⁹⁴(95-digit number)
22227752484058835341…58939389172731848961
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
4.445 Γ— 10⁹⁴(95-digit number)
44455504968117670682…17878778345463697919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.445 Γ— 10⁹⁴(95-digit number)
44455504968117670682…17878778345463697921
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
8.891 Γ— 10⁹⁴(95-digit number)
88911009936235341364…35757556690927395839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.891 Γ— 10⁹⁴(95-digit number)
88911009936235341364…35757556690927395841
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
1.778 Γ— 10⁹⁡(96-digit number)
17782201987247068272…71515113381854791679
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.778 Γ— 10⁹⁡(96-digit number)
17782201987247068272…71515113381854791681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2643269

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 446e90069d133f017ee548c62d141e06e5074646c46b833c569eb10a90a14c64

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 #2,643,269 on Chainz β†—
Circulating Supply:57,892,035 XPMΒ·at block #6,830,986 Β· updates every 60s
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