Block #83,670

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/26/2013, 7:46:10 AM · Difficulty 9.2684 · 6,712,999 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dc07b1919de36d2b41287c33b37c4caccf6d0ee9c42116000bcdb7e4cba00d18

View on Chainz ↗

Height

#83,670

Difficulty

9.268358

Transactions

Size

2.92 KB

Version

Bits

0944b324

Nonce

92,415

Timestamp

7/26/2013, 7:46:10 AM

Confirmations

6,712,999

Mined by

⛏️ P2SHALqKt6TXjB6VTWf6maKbF5SoKcmDLeyVea

Merkle Root

bf2b36cfad60d3d59597ef88e2560877839954b4059695e41a351b9356e77c0a

Transactions (3)

Coinbase1d722845ac823c…5aa624cb187972

1 in → 1 out11.6600 XPM109 B

ALqKt6TX…mDLeyVea

25e06e80ed5bdd…1b2121e0f91381

1 in → 2 out11.6700 XPM193 B

AbwHaVYX…7az1vYTw ARP8QpQi…sFuEcay7

a875bcb92ee308…145202981058fe

17 in → 2 out206.7600 XPM2.53 KB

AMP9Bsue…AqyZBtFe AL3jCG2K…moye79K3

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.579 × 10¹²⁴(125-digit number)

55798431314738124108…50659924226463015279

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

5.579 × 10¹²⁴(125-digit number)

55798431314738124108…50659924226463015279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.579 × 10¹²⁴(125-digit number)

55798431314738124108…50659924226463015281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.115 × 10¹²⁵(126-digit number)

11159686262947624821…01319848452926030559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.115 × 10¹²⁵(126-digit number)

11159686262947624821…01319848452926030561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.231 × 10¹²⁵(126-digit number)

22319372525895249643…02639696905852061119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.231 × 10¹²⁵(126-digit number)

22319372525895249643…02639696905852061121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

4.463 × 10¹²⁵(126-digit number)

44638745051790499286…05279393811704122239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.463 × 10¹²⁵(126-digit number)

44638745051790499286…05279393811704122241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

8.927 × 10¹²⁵(126-digit number)

89277490103580998573…10558787623408244479

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer