Block #299,046

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/7/2013, 5:27:51 PM · Difficulty 9.9920 · 6,507,010 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0f67179a4b60d94810f0ec0ce1846fb36a4e4e7f33f5737efa72b8c5960de985

View on Chainz ↗

Height

#299,046

Difficulty

9.992041

Transactions

Size

2.95 KB

Version

Bits

09fdf667

Nonce

149,909

Timestamp

12/7/2013, 5:27:51 PM

Confirmations

6,507,010

Mined by

⛏️ &aRZ.Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

055a53eee55c190b50392cb72a9ebc445183c2d0f0752d16ce2c3b3e3ac54474

Transactions (4)

Coinbaseeeb3614c1d2882…d5871ac27a4aea

1 in → 30 out9.9800 XPM1.06 KB

Ad9pSzHt…cpJ3y2zz AYtDvcGs…VuAcA7m7 AQwRN8bE…V8PsTcY9 AcM3ext6…Hwtj9Qp3 AToTBTPr…X3DsBU1U

74870c45fb8770…f1fe446630619f

3 in → 2 out82.6818 XPM522 B

AT4Ry5sg…BRSe23r8 ALEU1ast…hcNGir2o

572e95eefe2632…9c89c84df476e6

1 in → 2 out4496.6754 XPM225 B

APyCJcr1…QAhukZCb ALpDN118…cmDz8ivy

ff79ae6b319654…ec02a211dadfec

6 in → 8 out21.5208 XPM1.08 KB

AJgiYmMR…fJBp68k5 AM7Tr7C5…DnAdRwkh AGL4LiqG…EV8dqG2J AQPsd5v9…3JF1R7EY AXA2CgAY…sjcwKJeP

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.

4.042 × 10⁹⁷(98-digit number)

40422851023272987248…58875906503925939359

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

4.042 × 10⁹⁷(98-digit number)

40422851023272987248…58875906503925939359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.042 × 10⁹⁷(98-digit number)

40422851023272987248…58875906503925939361

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

8.084 × 10⁹⁷(98-digit number)

80845702046545974497…17751813007851878719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.084 × 10⁹⁷(98-digit number)

80845702046545974497…17751813007851878721

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

1.616 × 10⁹⁸(99-digit number)

16169140409309194899…35503626015703757439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.616 × 10⁹⁸(99-digit number)

16169140409309194899…35503626015703757441

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

3.233 × 10⁹⁸(99-digit number)

32338280818618389799…71007252031407514879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.233 × 10⁹⁸(99-digit number)

32338280818618389799…71007252031407514881

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

6.467 × 10⁹⁸(99-digit number)

64676561637236779598…42014504062815029759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.467 × 10⁹⁸(99-digit number)

64676561637236779598…42014504062815029761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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