Block #86,776

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 9:18:18 AM · Difficulty 9.2873 · 6,705,031 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

320981f72eb00c37b6b5eec11ae2e9e21a188f141166a7e9c282c6e4a59deb8c

View on Chainz ↗

Height

#86,776

Difficulty

9.287251

Transactions

Size

1.01 KB

Version

Bits

09498945

Nonce

123,797

Timestamp

7/28/2013, 9:18:18 AM

Confirmations

6,705,031

Merkle Root

403f243c626cbb509ebc78bab1c640af47ec5eb37da19d79117c847a322f4abb

Transactions (4)

Coinbase8c0fb653e500b9…d3e179ca4399a8

1 in → 1 out11.6100 XPM109 B

ALUMZnEW…WESC5ASW

bb93deec32e7e7…d5a1b100543fbb

1 in → 2 out11.6000 XPM225 B

AFqaE9Bb…Cp8gvdCb AZfo9pTv…JV8ajhKb

a7fbc562e13689…1ca531552e5ea1

1 in → 2 out3.3279 XPM226 B

AW3UZFYv…DFTf7Kh3 AeJpEDyZ…fh38vV2Y

bc2c280eaf2e1f…80f39896edac4a

2 in → 2 out5.0369 XPM374 B

AZFX5Ziq…FeXdQPzx ALCJdYBA…aBoknbAS

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.

3.069 × 10¹⁰⁸(109-digit number)

30690563566048303389…89346575110763891349

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

3.069 × 10¹⁰⁸(109-digit number)

30690563566048303389…89346575110763891349

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.069 × 10¹⁰⁸(109-digit number)

30690563566048303389…89346575110763891351

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

6.138 × 10¹⁰⁸(109-digit number)

61381127132096606778…78693150221527782699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.138 × 10¹⁰⁸(109-digit number)

61381127132096606778…78693150221527782701

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

1.227 × 10¹⁰⁹(110-digit number)

12276225426419321355…57386300443055565399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.227 × 10¹⁰⁹(110-digit number)

12276225426419321355…57386300443055565401

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

2.455 × 10¹⁰⁹(110-digit number)

24552450852838642711…14772600886111130799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.455 × 10¹⁰⁹(110-digit number)

24552450852838642711…14772600886111130801

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

4.910 × 10¹⁰⁹(110-digit number)

49104901705677285422…29545201772222261599

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