Block #158,085

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/10/2013, 2:49:02 AM · Difficulty 9.8681 · 6,645,444 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9f4c57f84f34a776a4ebee3b4708e805139fa3881b9cdbed0d174d767913a216

View on Chainz ↗

Height

#158,085

Difficulty

9.868059

Transactions

Size

570 B

Version

Bits

09de391e

Nonce

33,615

Timestamp

9/10/2013, 2:49:02 AM

Confirmations

6,645,444

Mined by

⛏️ P2SHAHnETrWi2hTEgsHntM5pwxzGXYU3CuFR9J

Merkle Root

282311d3c149471ad74eccb224ca95cecbf3ce4e18208ec50339c95bbef9ee4c

Transactions (2)

Coinbasebad462dad37491…0414e583b1723a

1 in → 1 out10.2600 XPM109 B

AHnETrWi…U3CuFR9J

08b522e3824762…656bc56b5ee015

2 in → 2 out68.4643 XPM373 B

Ab7iXvjf…LnFwMDZn ANScc6Hi…NQeHSjid

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.

1.544 × 10⁹⁰(91-digit number)

15440393559241356181…92419458826115062599

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

1.544 × 10⁹⁰(91-digit number)

15440393559241356181…92419458826115062599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.544 × 10⁹⁰(91-digit number)

15440393559241356181…92419458826115062601

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

3.088 × 10⁹⁰(91-digit number)

30880787118482712362…84838917652230125199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.088 × 10⁹⁰(91-digit number)

30880787118482712362…84838917652230125201

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

6.176 × 10⁹⁰(91-digit number)

61761574236965424724…69677835304460250399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.176 × 10⁹⁰(91-digit number)

61761574236965424724…69677835304460250401

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

1.235 × 10⁹¹(92-digit number)

12352314847393084944…39355670608920500799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.235 × 10⁹¹(92-digit number)

12352314847393084944…39355670608920500801

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

2.470 × 10⁹¹(92-digit number)

24704629694786169889…78711341217841001599

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