Block #2,123,705

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/19/2017, 10:50:23 AM · Difficulty 10.9171 · 4,717,979 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ba0ff70b4172de7d966675133d218a55d05f5a32e2a89ba8e6efb793f3ccaccb

View on Chainz ↗

Height

#2,123,705

Difficulty

10.917092

Transactions

Size

424 B

Version

Bits

0aeac686

Nonce

901,935,828

Timestamp

5/19/2017, 10:50:23 AM

Confirmations

4,717,979

Mined by

⛏️ P2SHAeq5kodiqLHQB7Wpw4SkbRbyyGnuqaP8Td

Merkle Root

d5b5ac8c65cd6ddb9f010344757cd41e58db21abc5e882132359f377caeba299

Transactions (2)

Coinbase3971cfc881c5ba…f3b0cc862204e7

1 in → 1 out8.3900 XPM109 B

Aeq5kodi…nuqaP8Td

508587eb5ea1e3…af75803c6f89b4

1 in → 2 out4.3202 XPM225 B

ANCGVTkJ…8AP3sQiR AXh11Exu…Ccq48SJm

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.

5.463 × 10⁹⁵(96-digit number)

54630076285994012202…03184085111947300799

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

5.463 × 10⁹⁵(96-digit number)

54630076285994012202…03184085111947300799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.463 × 10⁹⁵(96-digit number)

54630076285994012202…03184085111947300801

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

1.092 × 10⁹⁶(97-digit number)

10926015257198802440…06368170223894601599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.092 × 10⁹⁶(97-digit number)

10926015257198802440…06368170223894601601

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

2.185 × 10⁹⁶(97-digit number)

21852030514397604880…12736340447789203199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.185 × 10⁹⁶(97-digit number)

21852030514397604880…12736340447789203201

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

4.370 × 10⁹⁶(97-digit number)

43704061028795209761…25472680895578406399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.370 × 10⁹⁶(97-digit number)

43704061028795209761…25472680895578406401

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

8.740 × 10⁹⁶(97-digit number)

87408122057590419523…50945361791156812799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.740 × 10⁹⁶(97-digit number)

87408122057590419523…50945361791156812801

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 #2,123,705

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