Block #67,588

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 11:30:38 PM · Difficulty 8.9882 · 6,735,757 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8fab43541a89d9c20101bcb5d18fee2753b8daf3e4c4028afc5e4d9c4c379e01

View on Chainz ↗

Height

#67,588

Difficulty

8.988199

Transactions

Size

205 B

Version

Bits

08fcfa9d

Nonce

335

Timestamp

7/19/2013, 11:30:38 PM

Confirmations

6,735,757

Mined by

⛏️ P2SHAYGjxbdf98s9G3XmJfJE6yAGF5YFHt1cSm

Merkle Root

44e0bc42dbbe60fff67274cda9dbaffd39e8203677e0cddd723e12a3db136f73

Transactions (1)

Coinbase44e0bc42dbbe60…3e12a3db136f73

1 in → 1 out12.3600 XPM110 B

AYGjxbdf…YFHt1cSm

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.

1.005 × 10¹⁰⁶(107-digit number)

10056686912561859098…76123460124078613469

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

1.005 × 10¹⁰⁶(107-digit number)

10056686912561859098…76123460124078613469

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.005 × 10¹⁰⁶(107-digit number)

10056686912561859098…76123460124078613471

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

2.011 × 10¹⁰⁶(107-digit number)

20113373825123718196…52246920248157226939

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.011 × 10¹⁰⁶(107-digit number)

20113373825123718196…52246920248157226941

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

4.022 × 10¹⁰⁶(107-digit number)

40226747650247436392…04493840496314453879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.022 × 10¹⁰⁶(107-digit number)

40226747650247436392…04493840496314453881

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

8.045 × 10¹⁰⁶(107-digit number)

80453495300494872785…08987680992628907759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.045 × 10¹⁰⁶(107-digit number)

80453495300494872785…08987680992628907761

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

1.609 × 10¹⁰⁷(108-digit number)

16090699060098974557…17975361985257815519

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