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Home/Chain Registry/Block #2,678,742

Block #2,678,742

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/26/2018, 1:08:31 PM Β· Difficulty 11.6921 Β· 4,163,437 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
394fdc2a4beed8c5de87d75377e7150a718024da1814934e2b22ee0810577236
View on Chainz β†—

Difficulty

11.692077

Transactions

1

Size

202 B

Version

2

Bits

0bb12bf1

Nonce

802,030,678

Timestamp

5/26/2018, 1:08:31 PM

Confirmations

4,163,437

Merkle Root

ddbd5bd14ffa4ad3eff29cd0eec9613fd970a13063ab068c170a24877c8e295e
Transactions (1)
Coinbaseddbd5bd14ffa4a…0a24877c8e295e
1 in β†’ 1 out7.3000 XPM110 B
AKvh9wct…NbF9jXFL
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.

1.475 Γ— 10⁹⁸(99-digit number)
14759752439423107584…70725008129463418880
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
1.475 Γ— 10⁹⁸(99-digit number)
14759752439423107584…70725008129463418879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.475 Γ— 10⁹⁸(99-digit number)
14759752439423107584…70725008129463418881
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
2.951 Γ— 10⁹⁸(99-digit number)
29519504878846215168…41450016258926837759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.951 Γ— 10⁹⁸(99-digit number)
29519504878846215168…41450016258926837761
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
5.903 Γ— 10⁹⁸(99-digit number)
59039009757692430337…82900032517853675519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.903 Γ— 10⁹⁸(99-digit number)
59039009757692430337…82900032517853675521
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
1.180 Γ— 10⁹⁹(100-digit number)
11807801951538486067…65800065035707351039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.180 Γ— 10⁹⁹(100-digit number)
11807801951538486067…65800065035707351041
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
2.361 Γ— 10⁹⁹(100-digit number)
23615603903076972135…31600130071414702079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.361 Γ— 10⁹⁹(100-digit number)
23615603903076972135…31600130071414702081
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
4.723 Γ— 10⁹⁹(100-digit number)
47231207806153944270…63200260142829404159
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 2678742

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 394fdc2a4beed8c5de87d75377e7150a718024da1814934e2b22ee0810577236

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 #2,678,742 on Chainz β†—
Circulating Supply:57,981,824 XPMΒ·at block #6,842,178 Β· updates every 60s
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