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Block #104,488

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/8/2013, 2:08:48 AM Β· Difficulty 9.5575 Β· 6,695,653 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3d4ce7cb2f3a1a5c7a7c2fcabb805f01dd0be3f4b56123b7ddff6821346fd297
View on Chainz β†—

Height

#104,488

Difficulty

9.557532

Transactions

1

Size

200 B

Version

2

Bits

098eba72

Nonce

201,308

Timestamp

8/8/2013, 2:08:48 AM

Confirmations

6,695,653

Merkle Root

cdf4952c9fe0c8745c2d9d7b5887791d5fe65de4e69f2be77be9dd386a9570dc
Transactions (1)
Coinbasecdf4952c9fe0c8…e9dd386a9570dc
1 in β†’ 1 out10.9300 XPM109 B
AVTdASf7…wQZLqRtu
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.

2.370 Γ— 10⁹⁢(97-digit number)
23707289704356877241…67034730048498953020
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
2.370 Γ— 10⁹⁢(97-digit number)
23707289704356877241…67034730048498953019
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.370 Γ— 10⁹⁢(97-digit number)
23707289704356877241…67034730048498953021
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
4.741 Γ— 10⁹⁢(97-digit number)
47414579408713754482…34069460096997906039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.741 Γ— 10⁹⁢(97-digit number)
47414579408713754482…34069460096997906041
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
9.482 Γ— 10⁹⁢(97-digit number)
94829158817427508964…68138920193995812079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.482 Γ— 10⁹⁢(97-digit number)
94829158817427508964…68138920193995812081
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
1.896 Γ— 10⁹⁷(98-digit number)
18965831763485501792…36277840387991624159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.896 Γ— 10⁹⁷(98-digit number)
18965831763485501792…36277840387991624161
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
3.793 Γ— 10⁹⁷(98-digit number)
37931663526971003585…72555680775983248319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 104488

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 3d4ce7cb2f3a1a5c7a7c2fcabb805f01dd0be3f4b56123b7ddff6821346fd297

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 #104,488 on Chainz β†—
Circulating Supply:57,645,191 XPMΒ·at block #6,800,140 Β· updates every 60s
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