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Home/Chain Registry/Block #2,873,444

Block #2,873,444

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/9/2018, 2:56:04 AM Β· Difficulty 11.6651 Β· 3,966,373 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
35efebb95eaff3f95640fd62a3726d38965d888234555bfdf352d3e95865478c
View on Chainz β†—

Difficulty

11.665127

Transactions

1

Size

201 B

Version

2

Bits

0baa45bc

Nonce

218,102,186

Timestamp

10/9/2018, 2:56:04 AM

Confirmations

3,966,373

Merkle Root

14bbb1612d62d86999bb3265f6cb7af0e04a9865495edbb60888db94dbd731c6
Transactions (1)
Coinbase14bbb1612d62d8…88db94dbd731c6
1 in β†’ 1 out7.3400 XPM109 B
AdKzBqgU…6z4DUjJt
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.

8.349 Γ— 10⁹⁸(99-digit number)
83490232422868600260…70791515526615203840
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
8.349 Γ— 10⁹⁸(99-digit number)
83490232422868600260…70791515526615203839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.349 Γ— 10⁹⁸(99-digit number)
83490232422868600260…70791515526615203841
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
1.669 Γ— 10⁹⁹(100-digit number)
16698046484573720052…41583031053230407679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.669 Γ— 10⁹⁹(100-digit number)
16698046484573720052…41583031053230407681
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
3.339 Γ— 10⁹⁹(100-digit number)
33396092969147440104…83166062106460815359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.339 Γ— 10⁹⁹(100-digit number)
33396092969147440104…83166062106460815361
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
6.679 Γ— 10⁹⁹(100-digit number)
66792185938294880208…66332124212921630719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.679 Γ— 10⁹⁹(100-digit number)
66792185938294880208…66332124212921630721
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
1.335 Γ— 10¹⁰⁰(101-digit number)
13358437187658976041…32664248425843261439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.335 Γ— 10¹⁰⁰(101-digit number)
13358437187658976041…32664248425843261441
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
2.671 Γ— 10¹⁰⁰(101-digit number)
26716874375317952083…65328496851686522879
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 2873444

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 35efebb95eaff3f95640fd62a3726d38965d888234555bfdf352d3e95865478c

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 #2,873,444 on Chainz β†—
Circulating Supply:57,962,830 XPMΒ·at block #6,839,816 Β· updates every 60s
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