Block #88,068

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 8:22:57 AM · Difficulty 9.2740 · 6,703,739 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d54b3463fb01ce3a3d29db58c29670529931757aab72ce0bf888d6328f38032b

View on Chainz ↗

Height

#88,068

Difficulty

9.274044

Transactions

Size

916 B

Version

Bits

094627c6

Nonce

3,337

Timestamp

7/29/2013, 8:22:57 AM

Confirmations

6,703,739

Merkle Root

947e770d253e32ed439c577017b1938d020411c7ecafb67a4499e9d7e67d7ec9

Transactions (3)

Coinbasedb7de0a5771499…303784899ec01c

1 in → 1 out11.6300 XPM109 B

Ac9FAiLX…y5M5E5hz

7c4b5d474a9e71…7827f2976ee877

2 in → 2 out86.8697 XPM374 B

ALxZN753…Pv3xciR4 AMoyvsvP…EUfazodh

d478b5813d0e00…76d8b6200fbc5b

2 in → 1 out140.0000 XPM339 B

AdGYnqoY…pjMuwV34

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.

1.629 × 10¹⁰⁵(106-digit number)

16290560668235401719…06436608513347780679

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

1.629 × 10¹⁰⁵(106-digit number)

16290560668235401719…06436608513347780679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.629 × 10¹⁰⁵(106-digit number)

16290560668235401719…06436608513347780681

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

3.258 × 10¹⁰⁵(106-digit number)

32581121336470803438…12873217026695561359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.258 × 10¹⁰⁵(106-digit number)

32581121336470803438…12873217026695561361

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

6.516 × 10¹⁰⁵(106-digit number)

65162242672941606876…25746434053391122719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.516 × 10¹⁰⁵(106-digit number)

65162242672941606876…25746434053391122721

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

1.303 × 10¹⁰⁶(107-digit number)

13032448534588321375…51492868106782245439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.303 × 10¹⁰⁶(107-digit number)

13032448534588321375…51492868106782245441

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

2.606 × 10¹⁰⁶(107-digit number)

26064897069176642750…02985736213564490879

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