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Block #3,141,526

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/16/2019, 6:49:27 AM Β· Difficulty 11.3181 Β· 3,698,129 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
671fbda6e8e5e60db0c1497e56c270c09b7d7ab8d79a879fa6e4c08f0348c4c1
View on Chainz β†—

Difficulty

11.318104

Transactions

1

Size

200 B

Version

2

Bits

0b516f45

Nonce

1,170,917,930

Timestamp

4/16/2019, 6:49:27 AM

Confirmations

3,698,129

Merkle Root

2c106bbf9ec709289daf7b42c978c3698b0cb1baed373fd923aaf704208ecc9f
Transactions (1)
Coinbase2c106bbf9ec709…aaf704208ecc9f
1 in β†’ 1 out7.7900 XPM110 B
AbXwmGxD…4XXYP765
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.

7.345 Γ— 10⁹⁡(96-digit number)
73451736186825678360…00107890146969248000
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
7.345 Γ— 10⁹⁡(96-digit number)
73451736186825678360…00107890146969247999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.345 Γ— 10⁹⁡(96-digit number)
73451736186825678360…00107890146969248001
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
1.469 Γ— 10⁹⁢(97-digit number)
14690347237365135672…00215780293938495999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.469 Γ— 10⁹⁢(97-digit number)
14690347237365135672…00215780293938496001
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
2.938 Γ— 10⁹⁢(97-digit number)
29380694474730271344…00431560587876991999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.938 Γ— 10⁹⁢(97-digit number)
29380694474730271344…00431560587876992001
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
5.876 Γ— 10⁹⁢(97-digit number)
58761388949460542688…00863121175753983999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.876 Γ— 10⁹⁢(97-digit number)
58761388949460542688…00863121175753984001
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
1.175 Γ— 10⁹⁷(98-digit number)
11752277789892108537…01726242351507967999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.175 Γ— 10⁹⁷(98-digit number)
11752277789892108537…01726242351507968001
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
2.350 Γ— 10⁹⁷(98-digit number)
23504555579784217075…03452484703015935999
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 3141526

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 671fbda6e8e5e60db0c1497e56c270c09b7d7ab8d79a879fa6e4c08f0348c4c1

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 #3,141,526 on Chainz β†—
Circulating Supply:57,961,537 XPMΒ·at block #6,839,654 Β· updates every 60s
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