Block #158,018

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/10/2013, 1:27:36 AM · Difficulty 9.8684 · 6,638,793 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

91371edf8bae7686a11c5b595e9dd36791805edf48aaa15ddee9edc7ccca6e3b

View on Chainz ↗

Height

#158,018

Difficulty

9.868443

Transactions

Size

721 B

Version

Bits

09de5246

Nonce

202,384

Timestamp

9/10/2013, 1:27:36 AM

Confirmations

6,638,793

Mined by

⛏️ P2SHAT7i2C2XTUC3eAXfyQRCDXB3ic2LkmL1Zy

Merkle Root

42a29b77ca2163e6e8199dd334261a2412351ab0b52af6ff537bea25b33b69d5

Transactions (2)

Coinbase6341fe8af69894…389be802bc0dbd

1 in → 1 out10.2600 XPM109 B

AT7i2C2X…2LkmL1Zy

2d4a245cdfde91…302cecc93019b4

3 in → 2 out67.1001 XPM521 B

AGrVuhQG…dFkjBeEc AFxbUckd…6tupBuvz

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.

6.829 × 10⁹⁶(97-digit number)

68291175862964593656…79023807238691962879

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

6.829 × 10⁹⁶(97-digit number)

68291175862964593656…79023807238691962879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.829 × 10⁹⁶(97-digit number)

68291175862964593656…79023807238691962881

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

1.365 × 10⁹⁷(98-digit number)

13658235172592918731…58047614477383925759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.365 × 10⁹⁷(98-digit number)

13658235172592918731…58047614477383925761

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

2.731 × 10⁹⁷(98-digit number)

27316470345185837462…16095228954767851519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.731 × 10⁹⁷(98-digit number)

27316470345185837462…16095228954767851521

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

5.463 × 10⁹⁷(98-digit number)

54632940690371674925…32190457909535703039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.463 × 10⁹⁷(98-digit number)

54632940690371674925…32190457909535703041

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

1.092 × 10⁹⁸(99-digit number)

10926588138074334985…64380915819071406079

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