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Home/Chain Registry/Block #2,668,867

Block #2,668,867

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/19/2018, 8:31:57 PM Β· Difficulty 11.6768 Β· 4,173,522 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d4cd3fbdbf4ec968e8a70078ca050ec5995be23c7cce9d675d54e2dcc3567046
View on Chainz β†—

Difficulty

11.676822

Transactions

1

Size

200 B

Version

2

Bits

0bad4431

Nonce

1,543,118,793

Timestamp

5/19/2018, 8:31:57 PM

Confirmations

4,173,522

Merkle Root

dbc00103b9ad615d05a441248bb1598579bc3951630ac09f3f382faf4e0b2439
Transactions (1)
Coinbasedbc00103b9ad61…382faf4e0b2439
1 in β†’ 1 out7.3200 XPM110 B
AeGWyEve…QpAZGeLs
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.

5.274 Γ— 10⁹⁡(96-digit number)
52741712979088676216…08115322282933920000
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
5.274 Γ— 10⁹⁡(96-digit number)
52741712979088676216…08115322282933919999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.274 Γ— 10⁹⁡(96-digit number)
52741712979088676216…08115322282933920001
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
1.054 Γ— 10⁹⁢(97-digit number)
10548342595817735243…16230644565867839999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.054 Γ— 10⁹⁢(97-digit number)
10548342595817735243…16230644565867840001
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
2.109 Γ— 10⁹⁢(97-digit number)
21096685191635470486…32461289131735679999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.109 Γ— 10⁹⁢(97-digit number)
21096685191635470486…32461289131735680001
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
4.219 Γ— 10⁹⁢(97-digit number)
42193370383270940973…64922578263471359999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.219 Γ— 10⁹⁢(97-digit number)
42193370383270940973…64922578263471360001
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
8.438 Γ— 10⁹⁢(97-digit number)
84386740766541881947…29845156526942719999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.438 Γ— 10⁹⁢(97-digit number)
84386740766541881947…29845156526942720001
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
1.687 Γ— 10⁹⁷(98-digit number)
16877348153308376389…59690313053885439999
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 2668867

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 d4cd3fbdbf4ec968e8a70078ca050ec5995be23c7cce9d675d54e2dcc3567046

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 #2,668,867 on Chainz β†—
Circulating Supply:57,983,522 XPMΒ·at block #6,842,388 Β· updates every 60s
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