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Home/Chain Registry/Block #2,642,661

Block #2,642,661

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 7:44:59 PM Β· Difficulty 11.6600 Β· 4,188,271 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4947189cd1438d78345069a69b892dfd858fa6b3ac32ba031376335adf8ffb41
View on Chainz β†—

Difficulty

11.660036

Transactions

2

Size

575 B

Version

2

Bits

0ba8f823

Nonce

170,155,643

Timestamp

5/1/2018, 7:44:59 PM

Confirmations

4,188,271

Merkle Root

4eef556105705f57719a40584403c17c82c16c5117d3e78327795a1237bc86de
Transactions (2)
Coinbase89c8607fd943fc…9637ae9b060af1
1 in β†’ 1 out7.3500 XPM110 B
AevgGti1…sJPzsK51
7f8c60c2fa66f2…135dbfe5458a06
2 in β†’ 2 out8.4822 XPM375 B
APN4iKUA…YYqK7LLCAZ4UnHzJ…PH7NQioA
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.

8.268 Γ— 10⁹³(94-digit number)
82683633127897072219…70030171626034080000
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
8.268 Γ— 10⁹³(94-digit number)
82683633127897072219…70030171626034079999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.268 Γ— 10⁹³(94-digit number)
82683633127897072219…70030171626034080001
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
1.653 Γ— 10⁹⁴(95-digit number)
16536726625579414443…40060343252068159999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.653 Γ— 10⁹⁴(95-digit number)
16536726625579414443…40060343252068160001
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
3.307 Γ— 10⁹⁴(95-digit number)
33073453251158828887…80120686504136319999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.307 Γ— 10⁹⁴(95-digit number)
33073453251158828887…80120686504136320001
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
6.614 Γ— 10⁹⁴(95-digit number)
66146906502317657775…60241373008272639999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.614 Γ— 10⁹⁴(95-digit number)
66146906502317657775…60241373008272640001
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
1.322 Γ— 10⁹⁡(96-digit number)
13229381300463531555…20482746016545279999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.322 Γ— 10⁹⁡(96-digit number)
13229381300463531555…20482746016545280001
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
2.645 Γ— 10⁹⁡(96-digit number)
26458762600927063110…40965492033090559999
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 2642661

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 4947189cd1438d78345069a69b892dfd858fa6b3ac32ba031376335adf8ffb41

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 #2,642,661 on Chainz β†—
Circulating Supply:57,891,589 XPMΒ·at block #6,830,931 Β· updates every 60s
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