Block #88,339

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 1:36:57 PM · Difficulty 9.2680 · 6,706,261 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7042d670363cf6f560a58e65f83238c0383773a12a4fceee31074f44572fd27c

View on Chainz ↗

Height

#88,339

Difficulty

9.268024

Transactions

Size

2.86 KB

Version

Bits

09449d37

Nonce

636

Timestamp

7/29/2013, 1:36:57 PM

Confirmations

6,706,261

Mined by

⛏️ P2SHAPJPQwx8nKPoQRsJFLwi8pKxayajMwpQNv

Merkle Root

46906e1674f75be139a7f76014dc751e9ad836babf0644396f26f8a4f0667603

Transactions (4)

Coinbase72fd5b7543f117…359201717a585c

1 in → 1 out11.6700 XPM110 B

APJPQwx8…ajMwpQNv

8e3597bc878f55…4347d96edfdc0e

11 in → 1 out201.4300 XPM1.27 KB

AGfz3APU…kNJNtgfb

cf183471c24792…3dffd100485dfe

6 in → 2 out200.1530 XPM900 B

AXc99h1F…o4ftNX3T AeP4P5C5…vftevBwK

7e675dc5e89fe9…df62b8ea7794c7

3 in → 2 out222.0147 XPM523 B

AbmzUKNZ…VcJ3pauD AQvsUuNu…3pw3hMF5

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.

6.756 × 10¹⁰⁵(106-digit number)

67565934267936582753…90732431734567418119

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

6.756 × 10¹⁰⁵(106-digit number)

67565934267936582753…90732431734567418119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.756 × 10¹⁰⁵(106-digit number)

67565934267936582753…90732431734567418121

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

1.351 × 10¹⁰⁶(107-digit number)

13513186853587316550…81464863469134836239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.351 × 10¹⁰⁶(107-digit number)

13513186853587316550…81464863469134836241

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

2.702 × 10¹⁰⁶(107-digit number)

27026373707174633101…62929726938269672479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.702 × 10¹⁰⁶(107-digit number)

27026373707174633101…62929726938269672481

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

5.405 × 10¹⁰⁶(107-digit number)

54052747414349266203…25859453876539344959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.405 × 10¹⁰⁶(107-digit number)

54052747414349266203…25859453876539344961

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

1.081 × 10¹⁰⁷(108-digit number)

10810549482869853240…51718907753078689919

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