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Block #83,182

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/25/2013, 11:29:36 PM Β· Difficulty 9.2691 Β· 6,733,419 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9ea71dae0cf5f8b71a11260f4d0f0019b9269e824a8c92314c01c34871ea8661
View on Chainz β†—

Height

#83,182

Difficulty

9.269083

Transactions

1

Size

199 B

Version

2

Bits

0944e298

Nonce

75,340

Timestamp

7/25/2013, 11:29:36 PM

Confirmations

6,733,419

Mined by

⛏️ P2SHAeEXQxqG1a9HUoHobjrNQ1M2oHJ2q5dxWc

Merkle Root

91ccff4da5059a7d1f935c41b8668c2caf4e598f93b8bf99e72f3a903e2eee69
Transactions (1)
Coinbase91ccff4da5059a…2f3a903e2eee69
1 in β†’ 1 out11.6200 XPM109 B
AeEXQxqG…J2q5dxWc
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.

5.304 Γ— 10⁹³(94-digit number)
53045466713959637839…73972922984833800399
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
5.304 Γ— 10⁹³(94-digit number)
53045466713959637839…73972922984833800399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.304 Γ— 10⁹³(94-digit number)
53045466713959637839…73972922984833800401
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
1.060 Γ— 10⁹⁴(95-digit number)
10609093342791927567…47945845969667600799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.060 Γ— 10⁹⁴(95-digit number)
10609093342791927567…47945845969667600801
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
2.121 Γ— 10⁹⁴(95-digit number)
21218186685583855135…95891691939335201599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.121 Γ— 10⁹⁴(95-digit number)
21218186685583855135…95891691939335201601
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
4.243 Γ— 10⁹⁴(95-digit number)
42436373371167710271…91783383878670403199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.243 Γ— 10⁹⁴(95-digit number)
42436373371167710271…91783383878670403201
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
8.487 Γ— 10⁹⁴(95-digit number)
84872746742335420543…83566767757340806399
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:57,776,934 XPMΒ·at block #6,816,600 Β· updates every 60s
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