Block #3,144,101

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/18/2019, 1:27:46 AM · Difficulty 11.3206 · 3,698,784 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

392d1c1eaff54a4d15bc40ec93af5f0d037708677f396520fbf4a0c632959c49

View on Chainz ↗

Height

#3,144,101

Difficulty

11.320588

Transactions

Size

3.08 KB

Version

Bits

0b521208

Nonce

609,895,208

Timestamp

4/18/2019, 1:27:46 AM

Confirmations

3,698,784

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

e88ecff9ad6d31ccba0d9777879bb60d53f8f926866a9e612a465102d29580e5

Transactions (4)

Coinbasef97de10e69124c…a6cfb2bd715ea0

1 in → 1 out7.8300 XPM110 B

AUMQRepm…tAfKmdW1

25931717d07fe6…836a2cb5b6aa2a

7 in → 2 out54.6200 XPM872 B

AbXwmGxD…4XXYP765 ARx5pvS5…qXT1H2zv

d9b6aa2e47fda9…b8b25c5ab3e7b0

13 in → 2 out101.3900 XPM1.53 KB

AbXwmGxD…4XXYP765 AemY4Zt4…87UF1iHf

daf6d4133ba579…568545d6572601

3 in → 2 out0.1877 XPM522 B

AdTTnm5j…VXu4mLJo AbXwmGxD…4XXYP765

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.

6.081 × 10⁹⁴(95-digit number)

60815469122691778071…49915520752918608959

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

6.081 × 10⁹⁴(95-digit number)

60815469122691778071…49915520752918608959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.081 × 10⁹⁴(95-digit number)

60815469122691778071…49915520752918608961

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

1.216 × 10⁹⁵(96-digit number)

12163093824538355614…99831041505837217919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.216 × 10⁹⁵(96-digit number)

12163093824538355614…99831041505837217921

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

2.432 × 10⁹⁵(96-digit number)

24326187649076711228…99662083011674435839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.432 × 10⁹⁵(96-digit number)

24326187649076711228…99662083011674435841

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

4.865 × 10⁹⁵(96-digit number)

48652375298153422456…99324166023348871679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.865 × 10⁹⁵(96-digit number)

48652375298153422456…99324166023348871681

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

9.730 × 10⁹⁵(96-digit number)

97304750596306844913…98648332046697743359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.730 × 10⁹⁵(96-digit number)

97304750596306844913…98648332046697743361

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

1.946 × 10⁹⁶(97-digit number)

19460950119261368982…97296664093395486719

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 #3,144,101

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