Block #251,184

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 9:23:09 PM · Difficulty 9.9696 · 6,548,131 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5fc7844d729116613bc5e943980ef2827e0012db29ad9aa037fe916233e7cecd

View on Chainz ↗

Height

#251,184

Difficulty

9.969577

Transactions

Size

2.17 KB

Version

Bits

09f83639

Nonce

1,742

Timestamp

11/8/2013, 9:23:09 PM

Confirmations

6,548,131

Mined by

⛏️ 0aR}V0OAJzWx2VDShfKP9pKK3jZqTbn4sj4ZSMit5

Merkle Root

edef0ba79b92b79e93015522212052e13d8b423d1cab0986a36211193d2ef89e

Transactions (1)

Coinbaseedef0ba79b92b7…6211193d2ef89e

1 in → 61 out10.0200 XPM2.09 KB

AJzWx2VD…j4ZSMit5 AQtzUSwq…htAuF3yC AU9KdB9r…o5XC6WMy AKDTDDtx…iqvw9cdY ANo4YY1x…vnsPRDSU

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.

1.679 × 10⁹⁶(97-digit number)

16797585679825161571…59728272028628326399

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

1.679 × 10⁹⁶(97-digit number)

16797585679825161571…59728272028628326399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.679 × 10⁹⁶(97-digit number)

16797585679825161571…59728272028628326401

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

3.359 × 10⁹⁶(97-digit number)

33595171359650323143…19456544057256652799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.359 × 10⁹⁶(97-digit number)

33595171359650323143…19456544057256652801

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

6.719 × 10⁹⁶(97-digit number)

67190342719300646287…38913088114513305599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.719 × 10⁹⁶(97-digit number)

67190342719300646287…38913088114513305601

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

1.343 × 10⁹⁷(98-digit number)

13438068543860129257…77826176229026611199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.343 × 10⁹⁷(98-digit number)

13438068543860129257…77826176229026611201

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

2.687 × 10⁹⁷(98-digit number)

26876137087720258514…55652352458053222399

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