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Home/Chain Registry/Block #2,647,079

Block #2,647,079

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 5:27:06 PM Β· Difficulty 11.7565 Β· 4,195,092 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d8c4dab4c1cd25060c287e2c848a34bab5babbb641f667906af578ca5be2e5c5
View on Chainz β†—

Difficulty

11.756506

Transactions

1

Size

200 B

Version

2

Bits

0bc1aa66

Nonce

1,902,017,020

Timestamp

5/3/2018, 5:27:06 PM

Confirmations

4,195,092

Merkle Root

47c99eb7c14cd90137fad757a58269be62d6a37b98c0311e58329ece16200320
Transactions (1)
Coinbase47c99eb7c14cd9…329ece16200320
1 in β†’ 1 out7.2200 XPM110 B
AVauJZMG…Zy62ye3z
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.

5.454 Γ— 10⁹⁡(96-digit number)
54548774179932756103…17305859019986715520
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
5.454 Γ— 10⁹⁡(96-digit number)
54548774179932756103…17305859019986715519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.454 Γ— 10⁹⁡(96-digit number)
54548774179932756103…17305859019986715521
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
1.090 Γ— 10⁹⁢(97-digit number)
10909754835986551220…34611718039973431039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.090 Γ— 10⁹⁢(97-digit number)
10909754835986551220…34611718039973431041
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
2.181 Γ— 10⁹⁢(97-digit number)
21819509671973102441…69223436079946862079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.181 Γ— 10⁹⁢(97-digit number)
21819509671973102441…69223436079946862081
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
4.363 Γ— 10⁹⁢(97-digit number)
43639019343946204882…38446872159893724159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.363 Γ— 10⁹⁢(97-digit number)
43639019343946204882…38446872159893724161
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
8.727 Γ— 10⁹⁢(97-digit number)
87278038687892409765…76893744319787448319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.727 Γ— 10⁹⁢(97-digit number)
87278038687892409765…76893744319787448321
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
1.745 Γ— 10⁹⁷(98-digit number)
17455607737578481953…53787488639574896639
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 2647079

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 d8c4dab4c1cd25060c287e2c848a34bab5babbb641f667906af578ca5be2e5c5

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 #2,647,079 on Chainz β†—
Circulating Supply:57,981,758 XPMΒ·at block #6,842,170 Β· updates every 60s
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