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Home/Chain Registry/Block #2,639,315

Block #2,639,315

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/30/2018, 2:44:56 PM Β· Difficulty 11.5323 Β· 4,202,777 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9962e3960e858fb1c3fcc403a78e99e701b52e1831d86a5eeb38942950dba220
View on Chainz β†—

Difficulty

11.532326

Transactions

1

Size

199 B

Version

2

Bits

0b884680

Nonce

378,109,476

Timestamp

4/30/2018, 2:44:56 PM

Confirmations

4,202,777

Merkle Root

d491b4e3e738563efbd4deae193a9ae5506b8ffaea92c7f71d172a8ae9909959
Transactions (1)
Coinbased491b4e3e73856…172a8ae9909959
1 in β†’ 1 out7.5100 XPM110 B
AUWes8Kr…pXYWA66m
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.

1.136 Γ— 10⁹³(94-digit number)
11362290202310677836…21490345177312752160
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
1.136 Γ— 10⁹³(94-digit number)
11362290202310677836…21490345177312752159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.136 Γ— 10⁹³(94-digit number)
11362290202310677836…21490345177312752161
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
2.272 Γ— 10⁹³(94-digit number)
22724580404621355673…42980690354625504319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.272 Γ— 10⁹³(94-digit number)
22724580404621355673…42980690354625504321
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
4.544 Γ— 10⁹³(94-digit number)
45449160809242711346…85961380709251008639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.544 Γ— 10⁹³(94-digit number)
45449160809242711346…85961380709251008641
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
9.089 Γ— 10⁹³(94-digit number)
90898321618485422692…71922761418502017279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.089 Γ— 10⁹³(94-digit number)
90898321618485422692…71922761418502017281
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
1.817 Γ— 10⁹⁴(95-digit number)
18179664323697084538…43845522837004034559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.817 Γ— 10⁹⁴(95-digit number)
18179664323697084538…43845522837004034561
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
3.635 Γ— 10⁹⁴(95-digit number)
36359328647394169076…87691045674008069119
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 2639315

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 9962e3960e858fb1c3fcc403a78e99e701b52e1831d86a5eeb38942950dba220

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 #2,639,315 on Chainz β†—
Circulating Supply:57,981,122 XPMΒ·at block #6,842,091 Β· updates every 60s
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