Block #1,377,593

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/20/2015, 7:11:26 PM · Difficulty 10.8097 · 5,428,621 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4e991bb297cb0ac7cc62dbcffa646f73bba84701b47efb6e6ff795cde4c4ef5b

View on Chainz ↗

Height

#1,377,593

Difficulty

10.809715

Transactions

Size

5.04 KB

Version

Bits

0acf4976

Nonce

607,216,911

Timestamp

12/20/2015, 7:11:26 PM

Confirmations

5,428,621

Mined by

⛏️ P2SHAW216EFqiPKdvCRak4T8GVU1zdqVAWVKQ2

Merkle Root

98bfc2c9819c9bd44aff0ada1ade88cb150dae5bd877c0df68568122ed4a9811

Transactions (4)

Coinbaseb0dac1033cda2f…eb0427c904e412

1 in → 1 out8.6000 XPM109 B

AW216EFq…qVAWVKQ2

c4b73afa2d2deb…392800a054c57c

1 in → 30 out106.4667 XPM1.15 KB

ASTWMYyJ…ZP1k8yBD AMuYCqWB…sK6gjyWk AZhZSVVp…oSJWaM6a AeBpyz3j…R5Qj6rj5 AMMfQjgG…LYopNg2V

0baa2f01406c47…76da61bcc7535d

1 in → 51 out86.0228 XPM1.85 KB

AZCKZYH8…vgNRNs13 ASKojKCP…PYvZM4iF APpjGhP2…6d9X8ig7 ASG21nzq…iMYaGLq3 AS6u9fQK…HAp13QDV

bf47d789ea576b…ff6a679ab4d17c

1 in → 51 out49.4066 XPM1.85 KB

AK4usa1D…hbpdJPxn ARbmELZZ…D2EmA9eK ATkiCeum…91r8eHmY AXB2iJzr…VapWHkrP AFxh8SaK…YLUJLzm7

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.

3.363 × 10⁹⁴(95-digit number)

33638323292484256997…67947061642512178719

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

3.363 × 10⁹⁴(95-digit number)

33638323292484256997…67947061642512178719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.363 × 10⁹⁴(95-digit number)

33638323292484256997…67947061642512178721

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

6.727 × 10⁹⁴(95-digit number)

67276646584968513994…35894123285024357439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.727 × 10⁹⁴(95-digit number)

67276646584968513994…35894123285024357441

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

1.345 × 10⁹⁵(96-digit number)

13455329316993702798…71788246570048714879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.345 × 10⁹⁵(96-digit number)

13455329316993702798…71788246570048714881

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

2.691 × 10⁹⁵(96-digit number)

26910658633987405597…43576493140097429759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.691 × 10⁹⁵(96-digit number)

26910658633987405597…43576493140097429761

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

5.382 × 10⁹⁵(96-digit number)

53821317267974811195…87152986280194859519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.382 × 10⁹⁵(96-digit number)

53821317267974811195…87152986280194859521

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

1.076 × 10⁹⁶(97-digit number)

10764263453594962239…74305972560389719039

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