Block #3,181,557

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/14/2019, 9:12:36 AM · Difficulty 11.2590 · 3,657,381 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5f86e5e40665047ba59932a161415085e0057210f1e7e1a31e2b01c702b73398

View on Chainz ↗

Height

#3,181,557

Difficulty

11.258955

Transactions

Size

1.97 KB

Version

Bits

0b424ae8

Nonce

862,077,832

Timestamp

5/14/2019, 9:12:36 AM

Confirmations

3,657,381

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

58c1fed8652ad2493cf47d4451e0c6baade4c53d37904a35fcdc8d5eaa61f9e9

Transactions (5)

Coinbase95b645954b5a57…44f42b89d0f3b1

1 in → 1 out7.9200 XPM110 B

AUMQRepm…tAfKmdW1

4448d547135f07…de14a03458356c

7 in → 2 out50.6803 XPM912 B

AbXwmGxD…4XXYP765 ARx5pvS5…qXT1H2zv

956cac7c15e7b7…ee80350d907930

2 in → 2 out11.7036 XPM339 B

ASUcJnNi…eSt73bFU AbXwmGxD…4XXYP765

4db80cb93c1363…27f2692397a30f

2 in → 2 out13.5678 XPM341 B

AbXwmGxD…4XXYP765 AdGFnV3a…o6n2zX3x

236cf990fa35c7…5544aac79bbd45

1 in → 2 out3.5632 XPM226 B

AGbm9W17…Jvw6eg2t 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.

6.001 × 10⁹⁸(99-digit number)

60017395296753405732…03610816950142894079

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

6.001 × 10⁹⁸(99-digit number)

60017395296753405732…03610816950142894079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.001 × 10⁹⁸(99-digit number)

60017395296753405732…03610816950142894081

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

1.200 × 10⁹⁹(100-digit number)

12003479059350681146…07221633900285788159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.200 × 10⁹⁹(100-digit number)

12003479059350681146…07221633900285788161

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

2.400 × 10⁹⁹(100-digit number)

24006958118701362292…14443267800571576319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.400 × 10⁹⁹(100-digit number)

24006958118701362292…14443267800571576321

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

4.801 × 10⁹⁹(100-digit number)

48013916237402724585…28886535601143152639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.801 × 10⁹⁹(100-digit number)

48013916237402724585…28886535601143152641

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

9.602 × 10⁹⁹(100-digit number)

96027832474805449171…57773071202286305279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.602 × 10⁹⁹(100-digit number)

96027832474805449171…57773071202286305281

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

1.920 × 10¹⁰⁰(101-digit number)

19205566494961089834…15546142404572610559

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 #3,181,557

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