Block #2,138,047

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/30/2017, 1:09:16 PM · Difficulty 10.8858 · 4,679,781 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

58cab7cc7c90a278bebe79d1e9e07e16d763d1844d3830d376f5d360fb7ebc65

View on Chainz ↗

Height

#2,138,047

Difficulty

10.885844

Transactions

Size

5.48 KB

Version

Bits

0ae2c6a7

Nonce

634,345,265

Timestamp

5/30/2017, 1:09:16 PM

Confirmations

4,679,781

Mined by

⛏️ P2SHATzS2pidN3R6DpnjaNDABeJLt8brpsthai

Merkle Root

aab2956d0925e7d9e55643f21a3dd56045d3c556227277aedd787bd915519a52

Transactions (4)

Coinbasefb846ae1c28db9…6112a5b93956ca

1 in → 1 out8.5000 XPM109 B

ATzS2pid…brpsthai

449d1a9abc9a4c…0a71788dd3ee41

32 in → 2 out346.0872 XPM4.70 KB

AKp6SMft…9Kohodd4 AYh4JGrx…qskVXzqm

1cd574b5e804fd…64e524352e8cb6

2 in → 2 out2.1491 XPM375 B

AafsG5Ki…eeVfF2HT AUyCuGjK…ajKrKJpx

b218a28c50f353…462b954685e285

1 in → 2 out1.3564 XPM225 B

AaZTYNSU…ttpJbfTS ANwtSRNc…za9KnLoD

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.

2.310 × 10⁹⁴(95-digit number)

23109712514485298286…49096087234588408959

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

2.310 × 10⁹⁴(95-digit number)

23109712514485298286…49096087234588408959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.310 × 10⁹⁴(95-digit number)

23109712514485298286…49096087234588408961

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

4.621 × 10⁹⁴(95-digit number)

46219425028970596572…98192174469176817919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.621 × 10⁹⁴(95-digit number)

46219425028970596572…98192174469176817921

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

9.243 × 10⁹⁴(95-digit number)

92438850057941193145…96384348938353635839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.243 × 10⁹⁴(95-digit number)

92438850057941193145…96384348938353635841

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

1.848 × 10⁹⁵(96-digit number)

18487770011588238629…92768697876707271679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.848 × 10⁹⁵(96-digit number)

18487770011588238629…92768697876707271681

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

3.697 × 10⁹⁵(96-digit number)

36975540023176477258…85537395753414543359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.697 × 10⁹⁵(96-digit number)

36975540023176477258…85537395753414543361

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,138,047

Cookie Preferences