Block #153,559

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/7/2013, 2:16:06 AM · Difficulty 9.8633 · 6,652,706 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

398f640fb9fff20900a4097bca61259cc4aed7a19b2e18714165005fe6ae7f46

View on Chainz ↗

Height

#153,559

Difficulty

9.863277

Transactions

Size

1.21 KB

Version

Bits

09dcffc0

Nonce

76,052

Timestamp

9/7/2013, 2:16:06 AM

Confirmations

6,652,706

Mined by

⛏️ P2SHAaLrWjpuCAcVSwh3UXs9hmrdJsQmdcRbaT

Merkle Root

61a0df0c639ea91f792fb891d05782e578539e58e391f0f239782e1e772c4bba

Transactions (3)

Coinbase3b0b14c338f336…133a88f9359c93

1 in → 1 out10.2800 XPM109 B

AaLrWjpu…QmdcRbaT

405f8e2c095718…693da374be38e8

1 in → 2 out5.3933 XPM226 B

AZHeXEqt…i5CQsgj3 AdZCKwF2…4Pd38bXy

50a4f5954c0fab…957d715cfd12ab

5 in → 2 out2.0320 XPM816 B

AZ2HVrvK…1zcwkaFn AGJ7KxBM…SXRc3swJ

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.

2.238 × 10⁹⁴(95-digit number)

22388712979909848386…06331853291129802919

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

2.238 × 10⁹⁴(95-digit number)

22388712979909848386…06331853291129802919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.238 × 10⁹⁴(95-digit number)

22388712979909848386…06331853291129802921

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

4.477 × 10⁹⁴(95-digit number)

44777425959819696773…12663706582259605839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.477 × 10⁹⁴(95-digit number)

44777425959819696773…12663706582259605841

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

8.955 × 10⁹⁴(95-digit number)

89554851919639393547…25327413164519211679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.955 × 10⁹⁴(95-digit number)

89554851919639393547…25327413164519211681

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

1.791 × 10⁹⁵(96-digit number)

17910970383927878709…50654826329038423359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.791 × 10⁹⁵(96-digit number)

17910970383927878709…50654826329038423361

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

3.582 × 10⁹⁵(96-digit number)

35821940767855757419…01309652658076846719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.582 × 10⁹⁵(96-digit number)

35821940767855757419…01309652658076846721

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

Block #153,559

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