Block #1,364,137

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2015, 5:07:55 PM · Difficulty 10.8456 · 5,449,953 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

61836819fc92971d84dcf2ddd53e7cd7835eb0d153cd042ed70515e791a9b0f2

View on Chainz ↗

Height

#1,364,137

Difficulty

10.845624

Transactions

Size

1004 B

Version

Bits

0ad87ad3

Nonce

543,094,258

Timestamp

12/10/2015, 5:07:55 PM

Confirmations

5,449,953

Mined by

⛏️ P2SHAdUJcL9cTfj95BE31qWbQkmZ3XfdQ27Grd

Merkle Root

ab05e12f1bfac9296c1c25f3cfed4254d1d0a97dbddea155f6e3b046751ddac7

Transactions (2)

Coinbasee45fe7978e0532…a97f4542e40ad0

1 in → 1 out8.5000 XPM110 B

AdUJcL9c…fdQ27Grd

9366528fc86b86…0fc880ded6ea83

1 in → 19 out135.1928 XPM804 B

AdAQ18BM…AZe97t1s APpjGhP2…6d9X8ig7 AMjum32j…okZzjP2A AMoDoUQX…yFF5yULb AVXvAefY…XZMwJD1n

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.

3.453 × 10⁹⁵(96-digit number)

34530929601327008130…32407665014379375679

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

3.453 × 10⁹⁵(96-digit number)

34530929601327008130…32407665014379375679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.453 × 10⁹⁵(96-digit number)

34530929601327008130…32407665014379375681

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

6.906 × 10⁹⁵(96-digit number)

69061859202654016260…64815330028758751359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.906 × 10⁹⁵(96-digit number)

69061859202654016260…64815330028758751361

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

1.381 × 10⁹⁶(97-digit number)

13812371840530803252…29630660057517502719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.381 × 10⁹⁶(97-digit number)

13812371840530803252…29630660057517502721

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

2.762 × 10⁹⁶(97-digit number)

27624743681061606504…59261320115035005439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.762 × 10⁹⁶(97-digit number)

27624743681061606504…59261320115035005441

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

5.524 × 10⁹⁶(97-digit number)

55249487362123213008…18522640230070010879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.524 × 10⁹⁶(97-digit number)

55249487362123213008…18522640230070010881

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 #1,364,137

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