Block #153,049

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/6/2013, 6:01:22 PM · Difficulty 9.8629 · 6,643,068 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8d97bd287d2bde3102884575ba89fba2995f7c682745e871d61a2ee7e838cb61

View on Chainz ↗

Height

#153,049

Difficulty

9.862852

Transactions

Size

199 B

Version

Bits

09dce3e0

Nonce

100,011

Timestamp

9/6/2013, 6:01:22 PM

Confirmations

6,643,068

Mined by

⛏️ P2SHARzKAGFyC84BWrrsxzVJMjM6R6E5bJQ6Gf

Merkle Root

e1b59d33c73a10e27dd4c60682cecf6922a80a988050f52849af1ce5f7dbecd7

Transactions (1)

Coinbasee1b59d33c73a10…af1ce5f7dbecd7

1 in → 1 out10.2600 XPM109 B

ARzKAGFy…E5bJQ6Gf

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.

2.345 × 10⁹⁴(95-digit number)

23451615735610171810…22222148911308224479

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

2.345 × 10⁹⁴(95-digit number)

23451615735610171810…22222148911308224479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.345 × 10⁹⁴(95-digit number)

23451615735610171810…22222148911308224481

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

4.690 × 10⁹⁴(95-digit number)

46903231471220343621…44444297822616448959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.690 × 10⁹⁴(95-digit number)

46903231471220343621…44444297822616448961

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

9.380 × 10⁹⁴(95-digit number)

93806462942440687243…88888595645232897919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.380 × 10⁹⁴(95-digit number)

93806462942440687243…88888595645232897921

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

1.876 × 10⁹⁵(96-digit number)

18761292588488137448…77777191290465795839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.876 × 10⁹⁵(96-digit number)

18761292588488137448…77777191290465795841

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

3.752 × 10⁹⁵(96-digit number)

37522585176976274897…55554382580931591679

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