Block #1,139,335

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/4/2015, 8:05:31 AM · Difficulty 10.9357 · 5,704,029 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5bc53d083626a6a26e7b8a1bdec57cd9a0d32035f7c98de0b362f0f12a243aa0

View on Chainz ↗

Height

#1,139,335

Difficulty

10.935673

Transactions

Size

49.89 KB

Version

Bits

0aef884a

Nonce

46,480,384

Timestamp

7/4/2015, 8:05:31 AM

Confirmations

5,704,029

Mined by

⛏️ P2SHAbEzeBu12E8DBQ69pCrGJiCLABQZRSqUmD

Merkle Root

7bc573336b73e79830f7ee7114c64c5cf07c8534069bf0f61dbd2bef49f8bae9

Transactions (3)

Coinbasea8dce1515f9731…a6337afcfc244c

1 in → 1 out9.0200 XPM109 B

AbEzeBu1…QZRSqUmD

2d5a3fd4c330f3…a7a422c4df102e

292 in → 2 out220.1493 XPM42.26 KB

AW1kr72K…UTjJZYpc AUFmqDGk…wqWRc1Fk

148cc10aaf7921…6b69aa92a89a58

51 in → 2 out950.5162 XPM7.44 KB

Aaj3xjaL…ozAKLUBs AMP7EGhn…hgQDQGEc

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.

6.226 × 10⁹³(94-digit number)

62263647304630496710…82546617499960301229

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

6.226 × 10⁹³(94-digit number)

62263647304630496710…82546617499960301229

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.226 × 10⁹³(94-digit number)

62263647304630496710…82546617499960301231

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

1.245 × 10⁹⁴(95-digit number)

12452729460926099342…65093234999920602459

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.245 × 10⁹⁴(95-digit number)

12452729460926099342…65093234999920602461

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

2.490 × 10⁹⁴(95-digit number)

24905458921852198684…30186469999841204919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.490 × 10⁹⁴(95-digit number)

24905458921852198684…30186469999841204921

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

4.981 × 10⁹⁴(95-digit number)

49810917843704397368…60372939999682409839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.981 × 10⁹⁴(95-digit number)

49810917843704397368…60372939999682409841

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

9.962 × 10⁹⁴(95-digit number)

99621835687408794736…20745879999364819679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.962 × 10⁹⁴(95-digit number)

99621835687408794736…20745879999364819681

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 #1,139,335

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