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Home/Chain Registry/Block #2,648,315

Block #2,648,315

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/4/2018, 10:39:44 AM Β· Difficulty 11.7660 Β· 4,193,352 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
77e7982277bc6bf5ea61d2a2b4dc6dff88ad8eaa3483109ed2dc290aa557bc5e
View on Chainz β†—

Difficulty

11.765988

Transactions

1

Size

202 B

Version

2

Bits

0bc417c2

Nonce

1,376,655,349

Timestamp

5/4/2018, 10:39:44 AM

Confirmations

4,193,352

Merkle Root

3bfbb06a0671dd5633fea00dbf64bc49d986b15c19729f1b3d14e890e68e0311
Transactions (1)
Coinbase3bfbb06a0671dd…14e890e68e0311
1 in β†’ 1 out7.2100 XPM110 B
AdwodLVP…VmwGLJms
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.

4.318 Γ— 10⁹⁸(99-digit number)
43180135138794885265…44223313878450176000
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
4.318 Γ— 10⁹⁸(99-digit number)
43180135138794885265…44223313878450175999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.318 Γ— 10⁹⁸(99-digit number)
43180135138794885265…44223313878450176001
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
8.636 Γ— 10⁹⁸(99-digit number)
86360270277589770531…88446627756900351999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.636 Γ— 10⁹⁸(99-digit number)
86360270277589770531…88446627756900352001
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
1.727 Γ— 10⁹⁹(100-digit number)
17272054055517954106…76893255513800703999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.727 Γ— 10⁹⁹(100-digit number)
17272054055517954106…76893255513800704001
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
3.454 Γ— 10⁹⁹(100-digit number)
34544108111035908212…53786511027601407999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.454 Γ— 10⁹⁹(100-digit number)
34544108111035908212…53786511027601408001
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
6.908 Γ— 10⁹⁹(100-digit number)
69088216222071816425…07573022055202815999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.908 Γ— 10⁹⁹(100-digit number)
69088216222071816425…07573022055202816001
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
1.381 Γ— 10¹⁰⁰(101-digit number)
13817643244414363285…15146044110405631999
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 2648315

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 77e7982277bc6bf5ea61d2a2b4dc6dff88ad8eaa3483109ed2dc290aa557bc5e

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 #2,648,315 on Chainz β†—
Circulating Supply:57,977,725 XPMΒ·at block #6,841,666 Β· updates every 60s
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