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Home/Chain Registry/Block #2,667,137

Block #2,667,137

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/18/2018, 5:38:58 PM Β· Difficulty 11.6691 Β· 4,164,853 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
05fc5f0adf576328e40ca5d96157d8297b5d8960a9d44ba2d6a292b912433f24
View on Chainz β†—

Difficulty

11.669122

Transactions

1

Size

200 B

Version

2

Bits

0bab4b91

Nonce

1,528,284,926

Timestamp

5/18/2018, 5:38:58 PM

Confirmations

4,164,853

Merkle Root

329f4a6f5ed06f649df8cd7a9b018e2f09ef4367d4d05ba635f4b3baf2d048c6
Transactions (1)
Coinbase329f4a6f5ed06f…f4b3baf2d048c6
1 in β†’ 1 out7.3300 XPM110 B
Adqah8zh…1WwoHJ9t
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.

3.026 Γ— 10⁹⁡(96-digit number)
30261093476596874231…10653709184807900160
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
3.026 Γ— 10⁹⁡(96-digit number)
30261093476596874231…10653709184807900159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.026 Γ— 10⁹⁡(96-digit number)
30261093476596874231…10653709184807900161
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
6.052 Γ— 10⁹⁡(96-digit number)
60522186953193748462…21307418369615800319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.052 Γ— 10⁹⁡(96-digit number)
60522186953193748462…21307418369615800321
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
1.210 Γ— 10⁹⁢(97-digit number)
12104437390638749692…42614836739231600639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.210 Γ— 10⁹⁢(97-digit number)
12104437390638749692…42614836739231600641
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
2.420 Γ— 10⁹⁢(97-digit number)
24208874781277499384…85229673478463201279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.420 Γ— 10⁹⁢(97-digit number)
24208874781277499384…85229673478463201281
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
4.841 Γ— 10⁹⁢(97-digit number)
48417749562554998769…70459346956926402559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.841 Γ— 10⁹⁢(97-digit number)
48417749562554998769…70459346956926402561
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
9.683 Γ— 10⁹⁢(97-digit number)
96835499125109997539…40918693913852805119
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 2667137

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 05fc5f0adf576328e40ca5d96157d8297b5d8960a9d44ba2d6a292b912433f24

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 #2,667,137 on Chainz β†—
Circulating Supply:57,900,045 XPMΒ·at block #6,831,989 Β· updates every 60s
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