Block #152,382

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/6/2013, 7:18:59 AM · Difficulty 9.8623 · 6,637,345 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

538136f8e525dbac177dc4c2252a7f34e8b97fe86b0f80b90c6397cf4f337e1a

View on Chainz ↗

Height

#152,382

Difficulty

9.862258

Transactions

Size

3.05 KB

Version

Bits

09dcbcf0

Nonce

82,233

Timestamp

9/6/2013, 7:18:59 AM

Confirmations

6,637,345

Merkle Root

5dc98a00ab4fe91658cb20537265fb49018f2b80b36c43ab5043f1aabdd7e2f6

Transactions (4)

Coinbaseca95de57a557c1…c922fcb36e75cf

1 in → 1 out10.3200 XPM109 B

AX99MLNm…vtidqEwE

c3209497d60736…ba021da042f959

18 in → 1 out463.7560 XPM2.42 KB

ASnSjgQg…fewAaNPL

d1e6f64dd2596d…0e312791a625bb

1 in → 2 out8.2590 XPM225 B

AJYTh5cG…8qBnR2xz ARdEFcSb…mQoSgqJL

0bb66b8c7d6b16…edd31d498b97e1

1 in → 2 out8.2502 XPM225 B

AZUQUmKy…5ZKj7YT5 Abw8D7Bc…EioKVM91

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.

8.966 × 10⁹³(94-digit number)

89668964040324368347…68980982184113893799

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

8.966 × 10⁹³(94-digit number)

89668964040324368347…68980982184113893799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.966 × 10⁹³(94-digit number)

89668964040324368347…68980982184113893801

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

1.793 × 10⁹⁴(95-digit number)

17933792808064873669…37961964368227787599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.793 × 10⁹⁴(95-digit number)

17933792808064873669…37961964368227787601

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

3.586 × 10⁹⁴(95-digit number)

35867585616129747339…75923928736455575199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.586 × 10⁹⁴(95-digit number)

35867585616129747339…75923928736455575201

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

7.173 × 10⁹⁴(95-digit number)

71735171232259494678…51847857472911150399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.173 × 10⁹⁴(95-digit number)

71735171232259494678…51847857472911150401

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

1.434 × 10⁹⁵(96-digit number)

14347034246451898935…03695714945822300799

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