Block #158,920

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/10/2013, 6:14:07 PM · Difficulty 9.8657 · 6,636,727 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

32e0ee095413d158feb6e80f292b7fbdf8fc0def1cbdf5868ed41167279b1a54

View on Chainz ↗

Height

#158,920

Difficulty

9.865742

Transactions

Size

917 B

Version

Bits

09dda140

Nonce

4,152

Timestamp

9/10/2013, 6:14:07 PM

Confirmations

6,636,727

Mined by

⛏️ P2SHAZtkZfpRawx3u3CwQsLEQ6Hbc2FA2L7bTK

Merkle Root

3bc25bae78c2719f75ab8bf816774327b6ba12cf636146c0cc0bb49867325eb4

Transactions (2)

Coinbase4a8b51ae205233…e24a692fdc4daf

1 in → 1 out10.2700 XPM109 B

AZtkZfpR…FA2L7bTK

1cfbbec9cbbaec…1ffcd67b35856a

5 in → 2 out38.7460 XPM718 B

AUg3Ex4k…DpmGT4zh AGZvBxxa…shhkwtTn

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.

7.220 × 10⁹³(94-digit number)

72203744104667101787…58176883870403365439

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

7.220 × 10⁹³(94-digit number)

72203744104667101787…58176883870403365439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.220 × 10⁹³(94-digit number)

72203744104667101787…58176883870403365441

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

1.444 × 10⁹⁴(95-digit number)

14440748820933420357…16353767740806730879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.444 × 10⁹⁴(95-digit number)

14440748820933420357…16353767740806730881

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

2.888 × 10⁹⁴(95-digit number)

28881497641866840715…32707535481613461759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.888 × 10⁹⁴(95-digit number)

28881497641866840715…32707535481613461761

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

5.776 × 10⁹⁴(95-digit number)

57762995283733681430…65415070963226923519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.776 × 10⁹⁴(95-digit number)

57762995283733681430…65415070963226923521

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

1.155 × 10⁹⁵(96-digit number)

11552599056746736286…30830141926453847039

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