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Home/Chain Registry/Block #2,639,743

Block #2,639,743

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/30/2018, 6:25:43 PM Β· Difficulty 11.5512 Β· 4,204,043 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
117895315e620ccf34f4b5f38dbb0990220dce296fbe85ce0a80f7b9f7f90973
View on Chainz β†—

Difficulty

11.551219

Transactions

2

Size

427 B

Version

2

Bits

0b8d1cb7

Nonce

246,965,804

Timestamp

4/30/2018, 6:25:43 PM

Confirmations

4,204,043

Merkle Root

f2ca271cd91db3a3eb90e2b0a4dc1de0e5bc8d4f53f75d71dfc99457ef95ff2b
Transactions (2)
Coinbase7dd31d3cc65023…948e86bfd4722b
1 in β†’ 1 out7.4900 XPM110 B
Adqah8zh…1WwoHJ9t
1c8204307ff8af…44b3941f2fa90e
1 in β†’ 2 out1705.9600 XPM226 B
AYedwSS9…pToj9wCZARJQLHRp…K8XqtAkd
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.

1.131 Γ— 10⁹⁢(97-digit number)
11315218537752142686…97065722702340684800
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
1.131 Γ— 10⁹⁢(97-digit number)
11315218537752142686…97065722702340684799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.131 Γ— 10⁹⁢(97-digit number)
11315218537752142686…97065722702340684801
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
2.263 Γ— 10⁹⁢(97-digit number)
22630437075504285373…94131445404681369599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.263 Γ— 10⁹⁢(97-digit number)
22630437075504285373…94131445404681369601
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
4.526 Γ— 10⁹⁢(97-digit number)
45260874151008570746…88262890809362739199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.526 Γ— 10⁹⁢(97-digit number)
45260874151008570746…88262890809362739201
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
9.052 Γ— 10⁹⁢(97-digit number)
90521748302017141492…76525781618725478399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.052 Γ— 10⁹⁢(97-digit number)
90521748302017141492…76525781618725478401
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
1.810 Γ— 10⁹⁷(98-digit number)
18104349660403428298…53051563237450956799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.810 Γ— 10⁹⁷(98-digit number)
18104349660403428298…53051563237450956801
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
3.620 Γ— 10⁹⁷(98-digit number)
36208699320806856597…06103126474901913599
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 2639743

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 117895315e620ccf34f4b5f38dbb0990220dce296fbe85ce0a80f7b9f7f90973

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 #2,639,743 on Chainz β†—
Circulating Supply:57,994,664 XPMΒ·at block #6,843,785 Β· updates every 60s
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