Block #389,321

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2014, 10:05:13 AM · Difficulty 10.4194 · 6,408,881 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6be2946c1ad9fbc1fa59ba520e6ee6b3e3c41207d6e6ebd910a7877ac9778359

View on Chainz ↗

Height

#389,321

Difficulty

10.419424

Transactions

Size

4.28 KB

Version

Bits

0a6b5f62

Nonce

38,128

Timestamp

2/4/2014, 10:05:13 AM

Confirmations

6,408,881

Mined by

⛏️ P2SHAYZUGpXaKqJ144HRZuhFHsJcejW7UKsvcT

Merkle Root

d23349de37632df7d3ca48e0e7b20ff98939058fe8695e8caf868b5bfb7ff5ee

Transactions (5)

Coinbase835365e38177fc…49db37f8833073

1 in → 1 out9.2600 XPM109 B

AYZUGpXa…W7UKsvcT

f5f01671fac432…6c0b0af788b984

11 in → 1 out30.3122 XPM1.63 KB

AaaMW6Bg…qVVx5Fns

352bf0b6ed681f…96dcf35c93598b

4 in → 12 out36.9700 XPM873 B

ASZGYr4L…yo9EGKvo ATk8AZXy…cs2WLZjU AeGdqZdp…fbd4rTx5 ARaTCZXX…brdKR2Mj AeKNrjNj…1NEq95Ta

6bc3ee2aa644c9…4b95fe52c8b5a6

9 in → 2 out27.4244 XPM1.38 KB

ANECCeuu…mJ6mJJWN AYcMsTxv…n862Z4Z3

9aebc31ed8205a…5589bab80128d0

1 in → 2 out2.8499 XPM225 B

AbUCA4nr…WWvCaydG AXVS8Uwa…7MX7v6MT

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.

5.143 × 10¹⁰¹(102-digit number)

51434873393890347323…28445089889908633599

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

5.143 × 10¹⁰¹(102-digit number)

51434873393890347323…28445089889908633599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.143 × 10¹⁰¹(102-digit number)

51434873393890347323…28445089889908633601

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

1.028 × 10¹⁰²(103-digit number)

10286974678778069464…56890179779817267199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.028 × 10¹⁰²(103-digit number)

10286974678778069464…56890179779817267201

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

2.057 × 10¹⁰²(103-digit number)

20573949357556138929…13780359559634534399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.057 × 10¹⁰²(103-digit number)

20573949357556138929…13780359559634534401

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

4.114 × 10¹⁰²(103-digit number)

41147898715112277858…27560719119269068799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.114 × 10¹⁰²(103-digit number)

41147898715112277858…27560719119269068801

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

8.229 × 10¹⁰²(103-digit number)

82295797430224555717…55121438238538137599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.229 × 10¹⁰²(103-digit number)

82295797430224555717…55121438238538137601

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