Block #88,643

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 6:56:46 PM · Difficulty 9.2657 · 6,701,234 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fccacbe497e0fc116fd7a8da94285f7baa6a5d09c654b86b07aba0f1b1e2b280

View on Chainz ↗

Height

#88,643

Difficulty

9.265725

Transactions

Size

1.37 KB

Version

Bits

09440687

Nonce

258,279

Timestamp

7/29/2013, 6:56:46 PM

Confirmations

6,701,234

Merkle Root

88c8935956ae4511cedc5fa442bf71c9b7540af05bcb02e8a48faae4623d1206

Transactions (5)

Coinbase914f59b6a7ad70…ac28ffa2314ac3

1 in → 1 out11.6700 XPM109 B

AeEXQxqG…J2q5dxWc

1f44e560c562ba…aeb09ba63af847

1 in → 2 out2.1831 XPM226 B

Acvo1jg3…rE4TEtEk AS1Cqfvf…hB79WmgL

dacfc418e76de4…bb1dd40d94c43e

1 in → 2 out5.5280 XPM226 B

ANG86fDk…8oVbXjRA AZb9P6Us…2GpbnARv

1561d028bf9c93…f295e99fd49ea7

3 in → 2 out10.2754 XPM522 B

AeLxEQdx…Jugxqiqk AU55otxL…4KUcbBb9

e002807c0be31f…a58173a029bd7c

1 in → 2 out3.3667 XPM226 B

ALsgbymi…hBgnBNs6 Ac68xxU1…YrRNZ73p

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.

2.733 × 10⁹⁶(97-digit number)

27334608108705175648…50310877053467124919

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

2.733 × 10⁹⁶(97-digit number)

27334608108705175648…50310877053467124919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.733 × 10⁹⁶(97-digit number)

27334608108705175648…50310877053467124921

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

5.466 × 10⁹⁶(97-digit number)

54669216217410351297…00621754106934249839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.466 × 10⁹⁶(97-digit number)

54669216217410351297…00621754106934249841

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

1.093 × 10⁹⁷(98-digit number)

10933843243482070259…01243508213868499679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.093 × 10⁹⁷(98-digit number)

10933843243482070259…01243508213868499681

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

2.186 × 10⁹⁷(98-digit number)

21867686486964140519…02487016427736999359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.186 × 10⁹⁷(98-digit number)

21867686486964140519…02487016427736999361

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

4.373 × 10⁹⁷(98-digit number)

43735372973928281038…04974032855473998719

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