Block #3,168,340

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/4/2019, 10:46:05 PM · Difficulty 11.3108 · 3,674,416 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1275d14dad10d917f344bea4f9261c09a4757c591b67ae400d7286683a8e345f

View on Chainz ↗

Height

#3,168,340

Difficulty

11.310796

Transactions

Size

426 B

Version

Bits

0b4f904c

Nonce

1,812,137,429

Timestamp

5/4/2019, 10:46:05 PM

Confirmations

3,674,416

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

3fc29d84c37864bb3bdb72b80b52d8e8180159bcab920cde0637b54231333df4

Transactions (2)

Coinbased185e714a5af3f…e5901c8d1faf93

1 in → 1 out7.8100 XPM110 B

AbXwmGxD…4XXYP765

90f5002fd46dac…bfdb28224887b9

1 in → 2 out2.4650 XPM225 B

APQ9gg1V…H4v8MyZ4 AXq6UuhQ…swrTMgLC

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.

6.415 × 10⁹⁶(97-digit number)

64156122319135054964…02894906001668421759

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

6.415 × 10⁹⁶(97-digit number)

64156122319135054964…02894906001668421759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.415 × 10⁹⁶(97-digit number)

64156122319135054964…02894906001668421761

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

1.283 × 10⁹⁷(98-digit number)

12831224463827010992…05789812003336843519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.283 × 10⁹⁷(98-digit number)

12831224463827010992…05789812003336843521

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

2.566 × 10⁹⁷(98-digit number)

25662448927654021985…11579624006673687039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.566 × 10⁹⁷(98-digit number)

25662448927654021985…11579624006673687041

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

5.132 × 10⁹⁷(98-digit number)

51324897855308043971…23159248013347374079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.132 × 10⁹⁷(98-digit number)

51324897855308043971…23159248013347374081

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

1.026 × 10⁹⁸(99-digit number)

10264979571061608794…46318496026694748159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.026 × 10⁹⁸(99-digit number)

10264979571061608794…46318496026694748161

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

2.052 × 10⁹⁸(99-digit number)

20529959142123217588…92636992053389496319

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 #3,168,340

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