Block #92,470

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/1/2013, 5:36:47 PM · Difficulty 9.2031 · 6,717,671 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

abb02f1f692651df4c4c74dffd7e778c7e0d4895b4999ce43c887ed168111e87

View on Chainz ↗

Height

#92,470

Difficulty

9.203058

Transactions

Size

206 B

Version

Bits

0933fba2

Nonce

5,006

Timestamp

8/1/2013, 5:36:47 PM

Confirmations

6,717,671

Mined by

⛏️ P2SHAdGywN2wBfzQwTo7jGpVnaaNzDznNpTfrS

Merkle Root

0e05c9e0700499fc22a82a14a9efa774876e2fd01c2c4b7009bf3d514b0828b4

Transactions (1)

Coinbase0e05c9e0700499…bf3d514b0828b4

1 in → 1 out11.7900 XPM109 B

AdGywN2w…znNpTfrS

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.

1.719 × 10¹¹²(113-digit number)

17199699914832990047…66738611644417535599

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

1.719 × 10¹¹²(113-digit number)

17199699914832990047…66738611644417535599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.719 × 10¹¹²(113-digit number)

17199699914832990047…66738611644417535601

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

3.439 × 10¹¹²(113-digit number)

34399399829665980094…33477223288835071199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.439 × 10¹¹²(113-digit number)

34399399829665980094…33477223288835071201

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

6.879 × 10¹¹²(113-digit number)

68798799659331960189…66954446577670142399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.879 × 10¹¹²(113-digit number)

68798799659331960189…66954446577670142401

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

1.375 × 10¹¹³(114-digit number)

13759759931866392037…33908893155340284799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.375 × 10¹¹³(114-digit number)

13759759931866392037…33908893155340284801

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

2.751 × 10¹¹³(114-digit number)

27519519863732784075…67817786310680569599

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

Block #92,470

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