Block #88,075

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 8:36:37 AM · Difficulty 9.2737 · 6,707,762 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

979b74cf4a96376e0edafe49258e8db088045fe2a3e82c87d6608423790476d8

View on Chainz ↗

Height

#88,075

Difficulty

9.273666

Transactions

Size

1.47 KB

Version

Bits

09460ef2

Nonce

1,486

Timestamp

7/29/2013, 8:36:37 AM

Confirmations

6,707,762

Mined by

⛏️ P2SHAPUkenKawLq8RXXb4z3jvstwxDrp2YaVvt

Merkle Root

44b817be4191706f8b9b3764a44006613a06537708df161286f4f11c0a1abdf9

Transactions (3)

Coinbase60955d7a47f4ab…126ce74cddc3ac

1 in → 1 out11.6300 XPM110 B

APUkenKa…rp2YaVvt

ee9278e74b457a…7caee52e2ba127

3 in → 1 out35.0000 XPM487 B

AKYJBN2z…YRe233cD

116f35dd9cf227…f1b3fca286762e

5 in → 2 out251.8372 XPM818 B

AYGsdfzd…gB32Sap2 AMAQeFn7…VteciPjV

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.

1.403 × 10¹⁰¹(102-digit number)

14033305145269938688…09479259375849804819

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

1.403 × 10¹⁰¹(102-digit number)

14033305145269938688…09479259375849804819

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.403 × 10¹⁰¹(102-digit number)

14033305145269938688…09479259375849804821

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

2.806 × 10¹⁰¹(102-digit number)

28066610290539877377…18958518751699609639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.806 × 10¹⁰¹(102-digit number)

28066610290539877377…18958518751699609641

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

5.613 × 10¹⁰¹(102-digit number)

56133220581079754754…37917037503399219279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.613 × 10¹⁰¹(102-digit number)

56133220581079754754…37917037503399219281

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

1.122 × 10¹⁰²(103-digit number)

11226644116215950950…75834075006798438559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.122 × 10¹⁰²(103-digit number)

11226644116215950950…75834075006798438561

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

2.245 × 10¹⁰²(103-digit number)

22453288232431901901…51668150013596877119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.245 × 10¹⁰²(103-digit number)

22453288232431901901…51668150013596877121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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