Block #2,131,656

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/25/2017, 6:17:04 AM · Difficulty 10.9102 · 4,710,425 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a8035dfdd18176a39c77b9c788d6cc1ba7cd67948d2d9febc52cb9c816b614f8

View on Chainz ↗

Height

#2,131,656

Difficulty

10.910196

Transactions

Size

651 B

Version

Bits

0ae902a0

Nonce

1,286,558,950

Timestamp

5/25/2017, 6:17:04 AM

Confirmations

4,710,425

Mined by

⛏️ P2SHAYkWZ2NaqT8LfJHvaT1LYogxQuDgtsy3xj

Merkle Root

c10c08a83b952752aef7653b52bafa7617b8c1aa0ed1f37562fe86844b1aa0cf

Transactions (3)

Coinbasec19df93c22aea0…e05196eb2137ea

1 in → 1 out8.4100 XPM109 B

AYkWZ2Na…Dgtsy3xj

1915b03e52f02e…b2b1bff2f32c2b

1 in → 2 out126404.4402 XPM226 B

AXmCTHNy…ZJw8er6i ALuwGALM…8NGYvPPk

e2025a4fb48946…11a8840f94a113

1 in → 2 out19.4858 XPM226 B

AdiXGhio…3xcwfuiU AR22srsF…qKxzkZGY

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.

6.756 × 10⁹⁴(95-digit number)

67562909191402228200…07163485741195915039

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

6.756 × 10⁹⁴(95-digit number)

67562909191402228200…07163485741195915039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.756 × 10⁹⁴(95-digit number)

67562909191402228200…07163485741195915041

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

1.351 × 10⁹⁵(96-digit number)

13512581838280445640…14326971482391830079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.351 × 10⁹⁵(96-digit number)

13512581838280445640…14326971482391830081

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

2.702 × 10⁹⁵(96-digit number)

27025163676560891280…28653942964783660159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.702 × 10⁹⁵(96-digit number)

27025163676560891280…28653942964783660161

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

5.405 × 10⁹⁵(96-digit number)

54050327353121782560…57307885929567320319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.405 × 10⁹⁵(96-digit number)

54050327353121782560…57307885929567320321

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

1.081 × 10⁹⁶(97-digit number)

10810065470624356512…14615771859134640639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.081 × 10⁹⁶(97-digit number)

10810065470624356512…14615771859134640641

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 #2,131,656

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