Block #101,641

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/6/2013, 5:54:09 PM · Difficulty 9.4687 · 6,707,468 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

81cc4e9e2fac0043d4ee8d2efd898088d17f820f433eed1ed1617073df929c2b

View on Chainz ↗

Height

#101,641

Difficulty

9.468698

Transactions

Size

1.23 KB

Version

Bits

0977fc95

Nonce

102,480

Timestamp

8/6/2013, 5:54:09 PM

Confirmations

6,707,468

Mined by

⛏️ P2SHAezMwyLP2hpT3yh3LDZkydqkpsrTg7Eyfk

Merkle Root

7fc4830c493a5647631833b93ed7cc50a9ed92afab83da5299c2e565a6d34fdd

Transactions (4)

Coinbase7667a78b97f9b0…8456bbc66df972

1 in → 1 out11.1700 XPM109 B

AezMwyLP…rTg7Eyfk

01d87c9704a203…348f4691b171a7

3 in → 2 out23.0400 XPM455 B

AYQgZje2…fn4pgV5R AN2T3cet…JaG39i5Z

ff3736fa29a406…4f53543d1aaac4

1 in → 2 out6.3740 XPM226 B

ANdUMCLa…TzweiGyj AJv5WoqT…tqCRQqFk

7c8e7a390f4b24…9051794ef0292d

2 in → 2 out10.4289 XPM376 B

AWS3jSKC…smSDqntD Aah5Gkyr…qyQxdTg7

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.

4.602 × 10⁹⁴(95-digit number)

46023938945086555966…32855657883117228849

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

4.602 × 10⁹⁴(95-digit number)

46023938945086555966…32855657883117228849

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.602 × 10⁹⁴(95-digit number)

46023938945086555966…32855657883117228851

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

9.204 × 10⁹⁴(95-digit number)

92047877890173111933…65711315766234457699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.204 × 10⁹⁴(95-digit number)

92047877890173111933…65711315766234457701

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

1.840 × 10⁹⁵(96-digit number)

18409575578034622386…31422631532468915399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.840 × 10⁹⁵(96-digit number)

18409575578034622386…31422631532468915401

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

3.681 × 10⁹⁵(96-digit number)

36819151156069244773…62845263064937830799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.681 × 10⁹⁵(96-digit number)

36819151156069244773…62845263064937830801

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

7.363 × 10⁹⁵(96-digit number)

73638302312138489547…25690526129875661599

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

Block #101,641

Cookie Preferences