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Block #216,165

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/18/2013, 2:13:31 PM Β· Difficulty 9.9257 Β· 6,580,464 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
906a99be0ff21d625b2f8df51e5c8a476766e741cafd0bde5cfb57ed6297c8e8
View on Chainz β†—

Height

#216,165

Difficulty

9.925653

Transactions

2

Size

2.40 KB

Version

2

Bits

09ecf795

Nonce

309,773

Timestamp

10/18/2013, 2:13:31 PM

Confirmations

6,580,464

Mined by

⛏️ P2SHASG1EZdcVfsYmGCMbHmPPnScFHjDpBDXNJ

Merkle Root

7f1b47ba38326e91e1e8aea736d6fee9b93cf47353570a2fdbd7967ed518c5bc
Transactions (2)
Coinbasea6162b012861a0…481df755e1dd68
1 in β†’ 1 out10.1700 XPM109 B
ASG1EZdc…jDpBDXNJ
122ec2d403d45e…80405661110305
15 in β†’ 2 out156.0111 XPM2.21 KB
AWWFn2wt…447GdZy3Acd1BgN5…bE5c9NoN
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.

1.861 Γ— 10⁹⁴(95-digit number)
18611176313321204422…95762783016378531839
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
1.861 Γ— 10⁹⁴(95-digit number)
18611176313321204422…95762783016378531839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.861 Γ— 10⁹⁴(95-digit number)
18611176313321204422…95762783016378531841
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
3.722 Γ— 10⁹⁴(95-digit number)
37222352626642408844…91525566032757063679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.722 Γ— 10⁹⁴(95-digit number)
37222352626642408844…91525566032757063681
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
7.444 Γ— 10⁹⁴(95-digit number)
74444705253284817688…83051132065514127359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.444 Γ— 10⁹⁴(95-digit number)
74444705253284817688…83051132065514127361
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
1.488 Γ— 10⁹⁡(96-digit number)
14888941050656963537…66102264131028254719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.488 Γ— 10⁹⁡(96-digit number)
14888941050656963537…66102264131028254721
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
2.977 Γ— 10⁹⁡(96-digit number)
29777882101313927075…32204528262056509439
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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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
Cross-reference on Chainz Explorer
Circulating Supply:57,617,032 XPMΒ·at block #6,796,628 Β· updates every 60s
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