Block #2,131,355

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/25/2017, 1:23:03 AM · Difficulty 10.9101 · 4,709,310 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

287577571441386e6539a9414ec5e169c1a9befe11c81bb5f0f3a37f42349811

View on Chainz ↗

Height

#2,131,355

Difficulty

10.910092

Transactions

Size

1.22 KB

Version

Bits

0ae8fbc2

Nonce

326,283,500

Timestamp

5/25/2017, 1:23:03 AM

Confirmations

4,709,310

Mined by

⛏️ P2SHATmRcdeg5y6mbZKi6ocuadXWAN4JEgGvhA

Merkle Root

3fb76c4681517b8dbd1966de02cd27483fab73be6c3eec4b1b078d9ad8481033

Transactions (5)

Coinbase396056edeacfbc…d958973acc75a0

1 in → 1 out8.4300 XPM109 B

ATmRcdeg…4JEgGvhA

7b30bed7cc5ec5…55b21be1f2807a

1 in → 2 out179161.5685 XPM225 B

AeetsQEe…SbyhGjtW AFp7gSnM…bGRenBWt

f03db7af488275…f6bbc1e42fd4d1

1 in → 2 out64624.3922 XPM225 B

APjSqbMy…vyPCUyyR ANdP3v63…xS6orbx6

6913be8c49abf7…3dc0912fb011b6

2 in → 2 out15.9120 XPM373 B

AN24acsN…j8WmedDv AUF4LyGN…AH7djvvs

05060478c5af2c…40937abda139ca

1 in → 2 out61654.3822 XPM226 B

AaANa6kR…G7ngUSa8 AL4g3QwY…mpj35dTU

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.

2.297 × 10⁹⁷(98-digit number)

22978626365851233775…53383913662533411839

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

2.297 × 10⁹⁷(98-digit number)

22978626365851233775…53383913662533411839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.297 × 10⁹⁷(98-digit number)

22978626365851233775…53383913662533411841

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

4.595 × 10⁹⁷(98-digit number)

45957252731702467551…06767827325066823679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.595 × 10⁹⁷(98-digit number)

45957252731702467551…06767827325066823681

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

9.191 × 10⁹⁷(98-digit number)

91914505463404935102…13535654650133647359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.191 × 10⁹⁷(98-digit number)

91914505463404935102…13535654650133647361

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

1.838 × 10⁹⁸(99-digit number)

18382901092680987020…27071309300267294719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.838 × 10⁹⁸(99-digit number)

18382901092680987020…27071309300267294721

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

3.676 × 10⁹⁸(99-digit number)

36765802185361974041…54142618600534589439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.676 × 10⁹⁸(99-digit number)

36765802185361974041…54142618600534589441

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

7.353 × 10⁹⁸(99-digit number)

73531604370723948082…08285237201069178879

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

Block #2,131,355

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