Block #80,662

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 7:09:14 AM · Difficulty 9.2543 · 6,712,111 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

29169108a2f826fa257527214e97777fd98528192a9e096953544d37a23221e2

View on Chainz ↗

Height

#80,662

Difficulty

9.254339

Transactions

Size

1.58 KB

Version

Bits

09411c59

Nonce

104,366

Timestamp

7/24/2013, 7:09:14 AM

Confirmations

6,712,111

Merkle Root

03e5af080d276d442a88b9e72cf2e3f2268bc01f454338a6a05701ad5b0af550

Transactions (2)

Coinbaseaa3d3a8b83b7b1…6b36df0a4f9711

1 in → 1 out11.6800 XPM109 B

AbmC177F…pomdGgdX

3826e7eba8daaa…4f9663dc979c30

12 in → 1 out142.7000 XPM1.38 KB

AdNeXXkk…QpfXAns4

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.

1.216 × 10¹⁰⁷(108-digit number)

12160307170396568201…41173219058631097959

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

1.216 × 10¹⁰⁷(108-digit number)

12160307170396568201…41173219058631097959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.216 × 10¹⁰⁷(108-digit number)

12160307170396568201…41173219058631097961

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

2.432 × 10¹⁰⁷(108-digit number)

24320614340793136402…82346438117262195919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.432 × 10¹⁰⁷(108-digit number)

24320614340793136402…82346438117262195921

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

4.864 × 10¹⁰⁷(108-digit number)

48641228681586272804…64692876234524391839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.864 × 10¹⁰⁷(108-digit number)

48641228681586272804…64692876234524391841

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

9.728 × 10¹⁰⁷(108-digit number)

97282457363172545609…29385752469048783679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.728 × 10¹⁰⁷(108-digit number)

97282457363172545609…29385752469048783681

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

1.945 × 10¹⁰⁸(109-digit number)

19456491472634509121…58771504938097567359

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