Block #1,381,278

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/23/2015, 9:05:34 AM · Difficulty 10.8088 · 5,423,753 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e1516632cf7a166d6569d88dc099f6baaceeb5b144bc617e7a4c158979c9dcb0

View on Chainz ↗

Height

#1,381,278

Difficulty

10.808818

Transactions

Size

1.05 KB

Version

Bits

0acf0eba

Nonce

54,683,957

Timestamp

12/23/2015, 9:05:34 AM

Confirmations

5,423,753

Mined by

⛏️ P2SHAWGPvtRTQXbcdPqP3YLAaY8EN2CdH96bH5

Merkle Root

ca38407cfda48870ff1ae09e3c464a35a29726988ddd96f874c08387b3e6c715

Transactions (2)

Coinbase2bdbe45c385c2f…7e4756f1e11760

1 in → 1 out8.5600 XPM109 B

AWGPvtRT…CdH96bH5

19ff1f5fb70b54…e6c338ff7a59c0

1 in → 21 out209.8424 XPM872 B

AdxAPtjF…Tc9fy6tJ AcTyYdTB…Au15J5gk AQoahBZq…aH2WLCoJ AZGFjV3X…WZpygHs7 AFqAiWtG…JNZAjpHt

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.

3.583 × 10⁹⁴(95-digit number)

35832162046075157733…39701616138778905599

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

3.583 × 10⁹⁴(95-digit number)

35832162046075157733…39701616138778905599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.583 × 10⁹⁴(95-digit number)

35832162046075157733…39701616138778905601

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

7.166 × 10⁹⁴(95-digit number)

71664324092150315466…79403232277557811199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.166 × 10⁹⁴(95-digit number)

71664324092150315466…79403232277557811201

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

1.433 × 10⁹⁵(96-digit number)

14332864818430063093…58806464555115622399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.433 × 10⁹⁵(96-digit number)

14332864818430063093…58806464555115622401

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

2.866 × 10⁹⁵(96-digit number)

28665729636860126186…17612929110231244799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.866 × 10⁹⁵(96-digit number)

28665729636860126186…17612929110231244801

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

5.733 × 10⁹⁵(96-digit number)

57331459273720252373…35225858220462489599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.733 × 10⁹⁵(96-digit number)

57331459273720252373…35225858220462489601

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