Block #72,697

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 1:40:35 AM · Difficulty 8.9943 · 6,717,362 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

04ed02a1cc1a1cdc074a7067265e3278eb8d738968eb87d032628c2d693c2063

View on Chainz ↗

Height

#72,697

Difficulty

8.994270

Transactions

Size

1.05 KB

Version

Bits

08fe8879

Nonce

467

Timestamp

7/21/2013, 1:40:35 AM

Confirmations

6,717,362

Merkle Root

0c811e45813815b9c4541dd60c74f3fe6032f585c7b2b822270ffcbbed41ba7a

Transactions (3)

Coinbase7eda1a33ae8e74…cfc8ff442dc655

1 in → 1 out12.3600 XPM110 B

AK9a2aYB…b1UAyMo9

8c5d5082617ca2…8b09f67572618f

2 in → 2 out67.8800 XPM373 B

AGHdTqLJ…BGQAkaYq ALithVTY…q5cah22A

8791b8632183c9…cac344ff866701

4 in → 1 out49.3900 XPM498 B

AakWTnji…NVBZri5U

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.

3.289 × 10⁹⁴(95-digit number)

32899048709308565041…14945560216577409439

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

3.289 × 10⁹⁴(95-digit number)

32899048709308565041…14945560216577409439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.289 × 10⁹⁴(95-digit number)

32899048709308565041…14945560216577409441

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

6.579 × 10⁹⁴(95-digit number)

65798097418617130083…29891120433154818879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.579 × 10⁹⁴(95-digit number)

65798097418617130083…29891120433154818881

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

1.315 × 10⁹⁵(96-digit number)

13159619483723426016…59782240866309637759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.315 × 10⁹⁵(96-digit number)

13159619483723426016…59782240866309637761

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

2.631 × 10⁹⁵(96-digit number)

26319238967446852033…19564481732619275519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.631 × 10⁹⁵(96-digit number)

26319238967446852033…19564481732619275521

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

5.263 × 10⁹⁵(96-digit number)

52638477934893704066…39128963465238551039

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