Block #3,171,204

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/6/2019, 10:40:05 PM · Difficulty 11.3099 · 3,655,044 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3001b2ab962b2abeae4467115d0a535c454b6f16892b6817448c74262bb71f2c

View on Chainz ↗

Height

#3,171,204

Difficulty

11.309903

Transactions

Size

1.63 KB

Version

Bits

0b4f55d0

Nonce

508,621,613

Timestamp

5/6/2019, 10:40:05 PM

Confirmations

3,655,044

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

3a988072f22af97036f1d444b03fb679001650e2c0168e8ae14852db0e7e8047

Transactions (5)

Coinbase1260a2e2552902…f9529915ebbeb7

1 in → 1 out7.8400 XPM110 B

AbXwmGxD…4XXYP765

c8151b07389273…cf24fcd75ac6b7

2 in → 2 out15.5900 XPM304 B

APVKWthF…PMMxwRoz AYvC8EWN…y9e1vHwL

9e71f7b2dec863…64469444d97d65

2 in → 2 out15.5900 XPM307 B

AHQhLJgc…4nhNJ7Cw ALh3G4wq…cFPms2mF

f3e868c5aca232…6a29fad956a42d

3 in → 2 out10.1300 XPM486 B

AdqNKE8w…9vfbxZ2B AeHXpz5Q…WLPHByEV

5f0e4ad4764a53…8e20949ec5c7c2

2 in → 2 out11.1700 XPM374 B

AKM8nVAY…gE2YfRYY APVKWthF…PMMxwRoz

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.

1.758 × 10⁹⁸(99-digit number)

17586324287537109444…49731470033830215679

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

1.758 × 10⁹⁸(99-digit number)

17586324287537109444…49731470033830215679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.758 × 10⁹⁸(99-digit number)

17586324287537109444…49731470033830215681

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

3.517 × 10⁹⁸(99-digit number)

35172648575074218888…99462940067660431359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.517 × 10⁹⁸(99-digit number)

35172648575074218888…99462940067660431361

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

7.034 × 10⁹⁸(99-digit number)

70345297150148437776…98925880135320862719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.034 × 10⁹⁸(99-digit number)

70345297150148437776…98925880135320862721

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

1.406 × 10⁹⁹(100-digit number)

14069059430029687555…97851760270641725439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.406 × 10⁹⁹(100-digit number)

14069059430029687555…97851760270641725441

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

2.813 × 10⁹⁹(100-digit number)

28138118860059375110…95703520541283450879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.813 × 10⁹⁹(100-digit number)

28138118860059375110…95703520541283450881

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

5.627 × 10⁹⁹(100-digit number)

56276237720118750221…91407041082566901759

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 #3,171,204

Cookie Preferences