Block #2,147,160

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/5/2017, 4:06:24 PM · Difficulty 10.8926 · 4,692,971 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

25ad8f445141ad81770a0e2d5a87e3d511d0c5bd63bb5918b48f12c608f2544d

View on Chainz ↗

Height

#2,147,160

Difficulty

10.892640

Transactions

Size

1.36 KB

Version

Bits

0ae48411

Nonce

1,369,329,844

Timestamp

6/5/2017, 4:06:24 PM

Confirmations

4,692,971

Mined by

⛏️ P2SHAS6zex69MLi9DfCE3PPqKtwEXCJZRTcMki

Merkle Root

3ea87986227aa84b39d359abf4e7762e45bf70063b73349bb01ba3a00ac1a07a

Transactions (3)

Coinbasec8f560581f4d72…d134002d05eb13

1 in → 1 out8.4300 XPM109 B

AS6zex69…JZRTcMki

4805999abdc0f1…2a7df748620557

6 in → 2 out2872.9912 XPM967 B

AJ2vNg1F…MXs85ofM AQ8ZNq1V…VLmuKFor

4daec808bdcdf8…27634eb93640ee

1 in → 2 out119.3642 XPM225 B

AUY42adU…dJvHd8F9 AeTEzK2Y…Gj18uE8z

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.

3.235 × 10⁹⁴(95-digit number)

32354475406886885456…36164855370306705039

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

3.235 × 10⁹⁴(95-digit number)

32354475406886885456…36164855370306705039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.235 × 10⁹⁴(95-digit number)

32354475406886885456…36164855370306705041

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

6.470 × 10⁹⁴(95-digit number)

64708950813773770913…72329710740613410079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.470 × 10⁹⁴(95-digit number)

64708950813773770913…72329710740613410081

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

1.294 × 10⁹⁵(96-digit number)

12941790162754754182…44659421481226820159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.294 × 10⁹⁵(96-digit number)

12941790162754754182…44659421481226820161

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

2.588 × 10⁹⁵(96-digit number)

25883580325509508365…89318842962453640319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.588 × 10⁹⁵(96-digit number)

25883580325509508365…89318842962453640321

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

5.176 × 10⁹⁵(96-digit number)

51767160651019016730…78637685924907280639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.176 × 10⁹⁵(96-digit number)

51767160651019016730…78637685924907280641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.035 × 10⁹⁶(97-digit number)

10353432130203803346…57275371849814561279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,147,160

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