Block #3,086,623

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/10/2019, 8:27:33 AM · Difficulty 11.0378 · 3,756,374 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d7ad2a67c3dc8168cd472eb20b9865117c5a07da018b5ef889a8de654af98c7d

View on Chainz ↗

Height

#3,086,623

Difficulty

11.037847

Transactions

Size

575 B

Version

Bits

0b09b055

Nonce

1,848,279,374

Timestamp

3/10/2019, 8:27:33 AM

Confirmations

3,756,374

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

0de9e3b21806c948eea09bd8bc670ac2fb796793ed14b1e7a4f8221f85d49ba2

Transactions (2)

Coinbase6d9eb1d1e719e1…f44ef86517136d

1 in → 1 out8.2000 XPM110 B

AbXwmGxD…4XXYP765

7ada5603716040…d83ec8efb0ac76

2 in → 2 out30.0269 XPM375 B

AUooKPXK…fhVjHPc1 AeTHTL7A…vT1872bk

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.

2.408 × 10⁹³(94-digit number)

24087235774999461896…01109741341210903979

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

2.408 × 10⁹³(94-digit number)

24087235774999461896…01109741341210903979

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.408 × 10⁹³(94-digit number)

24087235774999461896…01109741341210903981

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

4.817 × 10⁹³(94-digit number)

48174471549998923793…02219482682421807959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.817 × 10⁹³(94-digit number)

48174471549998923793…02219482682421807961

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

9.634 × 10⁹³(94-digit number)

96348943099997847587…04438965364843615919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.634 × 10⁹³(94-digit number)

96348943099997847587…04438965364843615921

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

1.926 × 10⁹⁴(95-digit number)

19269788619999569517…08877930729687231839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.926 × 10⁹⁴(95-digit number)

19269788619999569517…08877930729687231841

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

3.853 × 10⁹⁴(95-digit number)

38539577239999139035…17755861459374463679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.853 × 10⁹⁴(95-digit number)

38539577239999139035…17755861459374463681

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

7.707 × 10⁹⁴(95-digit number)

77079154479998278070…35511722918748927359

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 #3,086,623

Cookie Preferences