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Home/Chain Registry/Block #2,801,897

Block #2,801,897

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/20/2018, 8:29:45 AM Β· Difficulty 11.6703 Β· 4,041,059 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dab7c1c9dd20480164cbfdd8618702fc82996751f6fc23b96580c84575e554a1
View on Chainz β†—

Difficulty

11.670276

Transactions

1

Size

201 B

Version

2

Bits

0bab9734

Nonce

1,046,363,467

Timestamp

8/20/2018, 8:29:45 AM

Confirmations

4,041,059

Merkle Root

da0d0135ed31bfc6d055dc352f8f48f8509500c465bcfece6f6173742c6e2a77
Transactions (1)
Coinbaseda0d0135ed31bf…6173742c6e2a77
1 in β†’ 1 out7.3300 XPM109 B
AKEfpYJy…DCwcyNVY
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.

2.515 Γ— 10⁹⁸(99-digit number)
25152607358856556770…70817462656641105920
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
2.515 Γ— 10⁹⁸(99-digit number)
25152607358856556770…70817462656641105919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.515 Γ— 10⁹⁸(99-digit number)
25152607358856556770…70817462656641105921
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
5.030 Γ— 10⁹⁸(99-digit number)
50305214717713113540…41634925313282211839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.030 Γ— 10⁹⁸(99-digit number)
50305214717713113540…41634925313282211841
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
1.006 Γ— 10⁹⁹(100-digit number)
10061042943542622708…83269850626564423679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.006 Γ— 10⁹⁹(100-digit number)
10061042943542622708…83269850626564423681
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
2.012 Γ— 10⁹⁹(100-digit number)
20122085887085245416…66539701253128847359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.012 Γ— 10⁹⁹(100-digit number)
20122085887085245416…66539701253128847361
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
4.024 Γ— 10⁹⁹(100-digit number)
40244171774170490832…33079402506257694719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.024 Γ— 10⁹⁹(100-digit number)
40244171774170490832…33079402506257694721
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
8.048 Γ— 10⁹⁹(100-digit number)
80488343548340981664…66158805012515389439
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 2801897

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 dab7c1c9dd20480164cbfdd8618702fc82996751f6fc23b96580c84575e554a1

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 #2,801,897 on Chainz β†—
Circulating Supply:57,988,001 XPMΒ·at block #6,842,955 Β· updates every 60s
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