Block #356,098

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2014, 1:26:02 PM · Difficulty 10.3717 · 6,448,909 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a6180bdfad4583dfe1d1845b5ba9bd8117a7f11fb6c8ee8f8b05896bcc2f93db

View on Chainz ↗

Height

#356,098

Difficulty

10.371661

Transactions

Size

217 B

Version

Bits

0a5f252b

Nonce

5,570

Timestamp

1/12/2014, 1:26:02 PM

Confirmations

6,448,909

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

f82b4d07b2c2b0e6e28eb7142b569c78f90c2cfd8a1934150eecc83a9df6458c

Transactions (1)

Coinbasef82b4d07b2c2b0…ecc83a9df6458c

1 in → 1 out9.2800 XPM116 B

AbwWkWZt…kawDhufa

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.

1.008 × 10¹²¹(122-digit number)

10081555882912344489…94721203978607001599

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

1.008 × 10¹²¹(122-digit number)

10081555882912344489…94721203978607001599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.008 × 10¹²¹(122-digit number)

10081555882912344489…94721203978607001601

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

2.016 × 10¹²¹(122-digit number)

20163111765824688978…89442407957214003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.016 × 10¹²¹(122-digit number)

20163111765824688978…89442407957214003201

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

4.032 × 10¹²¹(122-digit number)

40326223531649377956…78884815914428006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.032 × 10¹²¹(122-digit number)

40326223531649377956…78884815914428006401

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

8.065 × 10¹²¹(122-digit number)

80652447063298755912…57769631828856012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.065 × 10¹²¹(122-digit number)

80652447063298755912…57769631828856012801

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

1.613 × 10¹²²(123-digit number)

16130489412659751182…15539263657712025599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.613 × 10¹²²(123-digit number)

16130489412659751182…15539263657712025601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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