Block #67,093

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 8:56:11 PM · Difficulty 8.9874 · 6,732,391 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ed188db8b5adcc2583d04992932ba68e7588b2a8398fa661bf696cee4f3862fd

View on Chainz ↗

Height

#67,093

Difficulty

8.987386

Transactions

Size

364 B

Version

Bits

08fcc54c

Nonce

644

Timestamp

7/19/2013, 8:56:11 PM

Confirmations

6,732,391

Mined by

⛏️ P2SHAXWphP8TebwduDiYciZuMF4H344trwmtBM

Merkle Root

e6d81b8c88f2973176aa460402e7088580f9079f22300603ce81f8e3d1397299

Transactions (2)

Coinbaseb7935c58ae8fe9…67f15511e4b25e

1 in → 1 out12.3700 XPM109 B

AXWphP8T…4trwmtBM

0b0b9b997c7ef4…0349c116d36f1f

1 in → 1 out12.3700 XPM159 B

Ab1hhPzi…URi5woLf

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.

7.745 × 10¹⁰⁸(109-digit number)

77450536792287070770…36674471910120757399

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

7.745 × 10¹⁰⁸(109-digit number)

77450536792287070770…36674471910120757399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.745 × 10¹⁰⁸(109-digit number)

77450536792287070770…36674471910120757401

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

1.549 × 10¹⁰⁹(110-digit number)

15490107358457414154…73348943820241514799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.549 × 10¹⁰⁹(110-digit number)

15490107358457414154…73348943820241514801

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

3.098 × 10¹⁰⁹(110-digit number)

30980214716914828308…46697887640483029599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.098 × 10¹⁰⁹(110-digit number)

30980214716914828308…46697887640483029601

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

6.196 × 10¹⁰⁹(110-digit number)

61960429433829656616…93395775280966059199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.196 × 10¹⁰⁹(110-digit number)

61960429433829656616…93395775280966059201

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

1.239 × 10¹¹⁰(111-digit number)

12392085886765931323…86791550561932118399

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