Block #160,869

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/12/2013, 6:23:11 AM · Difficulty 9.8598 · 6,644,216 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f8720d1084c93c41f40a38be5ea1f4a2c1b4ba4a041a7a260b05ee6dc0be5b5

View on Chainz ↗

Height

#160,869

Difficulty

9.859822

Transactions

Size

198 B

Version

Bits

09dc1d4e

Nonce

19,987

Timestamp

9/12/2013, 6:23:11 AM

Confirmations

6,644,216

Mined by

⛏️ P2SHAX99MLNmm1FbkFRt6WY4Zu9rUBvtidqEwE

Merkle Root

3507a0ab66e03960bf65c53635c58a2e9e28b3cda07a3893a2e4635052b4ed6c

Transactions (1)

Coinbase3507a0ab66e039…e4635052b4ed6c

1 in → 1 out10.2700 XPM109 B

AX99MLNm…vtidqEwE

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.

3.631 × 10⁹¹(92-digit number)

36319493076038148583…75756046216375133749

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

3.631 × 10⁹¹(92-digit number)

36319493076038148583…75756046216375133749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.631 × 10⁹¹(92-digit number)

36319493076038148583…75756046216375133751

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

7.263 × 10⁹¹(92-digit number)

72638986152076297167…51512092432750267499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.263 × 10⁹¹(92-digit number)

72638986152076297167…51512092432750267501

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

1.452 × 10⁹²(93-digit number)

14527797230415259433…03024184865500534999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.452 × 10⁹²(93-digit number)

14527797230415259433…03024184865500535001

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

2.905 × 10⁹²(93-digit number)

29055594460830518867…06048369731001069999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.905 × 10⁹²(93-digit number)

29055594460830518867…06048369731001070001

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

5.811 × 10⁹²(93-digit number)

58111188921661037734…12096739462002139999

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