Block #379,809

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2014, 6:55:23 PM · Difficulty 10.4201 · 6,423,859 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b33eaa8b01f8e24d0ee78a9ce4b8849b4b8abb60bb9ec710341fae0af9853b1e

View on Chainz ↗

Height

#379,809

Difficulty

10.420068

Transactions

Size

650 B

Version

Bits

0a6b8994

Nonce

221,630

Timestamp

1/28/2014, 6:55:23 PM

Confirmations

6,423,859

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a29f146568f2a3ca0f1a69db9e539d4c97ec4722fabcfa866a03716019d61bd5

Transactions (3)

Coinbasea5569d830bc844…9a2119d27bbf9b

1 in → 1 out9.2200 XPM110 B

AeKNrjNj…1NEq95Ta

0074055f16cb7a…37359fea3f768a

1 in → 2 out5.0225 XPM225 B

AVLTe17z…YZjG3pgV APipUeHf…kh7dJESD

0453e3d543fc8d…8483dfdd5ea015

1 in → 2 out3.1169 XPM226 B

AWxj3gef…33g9DysR AZJe4Bxu…Ztr9u4dc

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.

9.933 × 10⁹¹(92-digit number)

99333398405353035033…45344722398777669499

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

9.933 × 10⁹¹(92-digit number)

99333398405353035033…45344722398777669499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.933 × 10⁹¹(92-digit number)

99333398405353035033…45344722398777669501

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

1.986 × 10⁹²(93-digit number)

19866679681070607006…90689444797555338999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.986 × 10⁹²(93-digit number)

19866679681070607006…90689444797555339001

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

3.973 × 10⁹²(93-digit number)

39733359362141214013…81378889595110677999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.973 × 10⁹²(93-digit number)

39733359362141214013…81378889595110678001

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

7.946 × 10⁹²(93-digit number)

79466718724282428027…62757779190221355999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.946 × 10⁹²(93-digit number)

79466718724282428027…62757779190221356001

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

1.589 × 10⁹³(94-digit number)

15893343744856485605…25515558380442711999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.589 × 10⁹³(94-digit number)

15893343744856485605…25515558380442712001

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