Block #154,716

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/7/2013, 8:45:15 PM · Difficulty 9.8647 · 6,656,205 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aba46496f31d9e70348f35161ce7b8a5bdfb7da35771756b72d30e02c6837576

View on Chainz ↗

Height

#154,716

Difficulty

9.864735

Transactions

Size

913 B

Version

Bits

09dd5f49

Nonce

16,630

Timestamp

9/7/2013, 8:45:15 PM

Confirmations

6,656,205

Mined by

⛏️ P2SHAdktB7K3giE6KLpKCLiWyYRnn6uWFqnnCf

Merkle Root

0c10c08d1d27ab15838fd736f8335bb37b5162d14ae80fced4854ec647531fce

Transactions (3)

Coinbase92281e87db686c…ccef24ae3c764f

1 in → 1 out10.2800 XPM109 B

AdktB7K3…uWFqnnCf

f3e46923cc9ac2…955ea13bd6aea3

3 in → 2 out200.0107 XPM522 B

Aanv4FuE…YtHL3Sw9 AXCoN6AA…zcf98WDF

d277b2a331e771…fe45442c6a2b07

1 in → 2 out10.2600 XPM192 B

AFz9fXym…wh4UqpkL ALZafa9u…GpDskj8z

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.

3.358 × 10⁹⁴(95-digit number)

33583404544815029127…23026226995416589759

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

3.358 × 10⁹⁴(95-digit number)

33583404544815029127…23026226995416589759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.358 × 10⁹⁴(95-digit number)

33583404544815029127…23026226995416589761

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

6.716 × 10⁹⁴(95-digit number)

67166809089630058254…46052453990833179519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.716 × 10⁹⁴(95-digit number)

67166809089630058254…46052453990833179521

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

1.343 × 10⁹⁵(96-digit number)

13433361817926011650…92104907981666359039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.343 × 10⁹⁵(96-digit number)

13433361817926011650…92104907981666359041

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

2.686 × 10⁹⁵(96-digit number)

26866723635852023301…84209815963332718079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.686 × 10⁹⁵(96-digit number)

26866723635852023301…84209815963332718081

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

5.373 × 10⁹⁵(96-digit number)

53733447271704046603…68419631926665436159

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

Block #154,716

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