Block #94,484

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/3/2013, 3:14:50 AM · Difficulty 9.2030 · 6,695,299 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8416b6de490fdf35d12c8155c9e765727a5d6f371cca5e8db99bcfc7558b3572

View on Chainz ↗

Height

#94,484

Difficulty

9.203004

Transactions

Size

1.89 KB

Version

Bits

0933f817

Nonce

1,114

Timestamp

8/3/2013, 3:14:50 AM

Confirmations

6,695,299

Merkle Root

d774a1ecb688ea548c64f0630a1feceb85560b1405eeb546415c7131ef0f680d

Transactions (5)

Coinbase5222c99f66d893…cf8c9403b3d269

1 in → 1 out11.8300 XPM110 B

AJL3J8EV…QzQDcxf1

332d82c430a5b0…b8f9a017fb0081

4 in → 2 out68.7260 XPM670 B

AXXD9rC2…Vb5reFe7 AZhsX97Z…GMcjdZLL

37c2279a2c3f1c…2e4340acd1e2ba

1 in → 1 out11.5700 XPM157 B

AUyL3rcf…PuULqq4T

61bb080f457d18…cbf87b79cb510a

2 in → 2 out99.9791 XPM374 B

AYxoT5K3…VLfpXK9w AWGVm16F…tiqUJbv4

383494e12039be…6ef1358493d62d

3 in → 2 out6.0249 XPM520 B

Aab9Yugh…rcYmYYyq APkkcELq…s4wpFZKX

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.

4.892 × 10¹¹⁸(119-digit number)

48927367867199743725…48948584607849907619

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

4.892 × 10¹¹⁸(119-digit number)

48927367867199743725…48948584607849907619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.892 × 10¹¹⁸(119-digit number)

48927367867199743725…48948584607849907621

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

9.785 × 10¹¹⁸(119-digit number)

97854735734399487450…97897169215699815239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.785 × 10¹¹⁸(119-digit number)

97854735734399487450…97897169215699815241

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

1.957 × 10¹¹⁹(120-digit number)

19570947146879897490…95794338431399630479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.957 × 10¹¹⁹(120-digit number)

19570947146879897490…95794338431399630481

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

3.914 × 10¹¹⁹(120-digit number)

39141894293759794980…91588676862799260959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.914 × 10¹¹⁹(120-digit number)

39141894293759794980…91588676862799260961

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

7.828 × 10¹¹⁹(120-digit number)

78283788587519589960…83177353725598521919

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