Block #386,644

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/2/2014, 2:23:33 PM · Difficulty 10.4120 · 6,421,691 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

377a6cd4dc3dd5c9ab512954afe0f973f43fe853df3afd701e661a4fb430cfa0

View on Chainz ↗

Height

#386,644

Difficulty

10.412016

Transactions

Size

885 B

Version

Bits

0a6979e4

Nonce

7,321

Timestamp

2/2/2014, 2:23:33 PM

Confirmations

6,421,691

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

944db4c31e40b135df21fa18349676340180cb0ee7d851a2ee39c1669c84f49c

Transactions (4)

Coinbase3315cfca542d96…975353d3443751

1 in → 1 out9.2400 XPM116 B

AbwWkWZt…kawDhufa

295caaf2d31d2b…d415533b8c5499

1 in → 2 out286.8427 XPM227 B

ATywqceM…8FizGnHx Abtu91vu…wE3wLHJX

0892b6c7c92cb8…17d5a24575d5d6

1 in → 2 out4743.3964 XPM226 B

AYXcB27Y…WroVpy7z AbLertqB…WUAPYd2k

6dd05faf6a5dad…6665751eda2589

1 in → 2 out3.1134 XPM225 B

ALGCw9at…WNhrSMx8 AXuZzeRT…GrhZB71n

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.

3.699 × 10⁹⁶(97-digit number)

36990440299617653953…74278336936304645999

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

3.699 × 10⁹⁶(97-digit number)

36990440299617653953…74278336936304645999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.699 × 10⁹⁶(97-digit number)

36990440299617653953…74278336936304646001

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

7.398 × 10⁹⁶(97-digit number)

73980880599235307907…48556673872609291999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.398 × 10⁹⁶(97-digit number)

73980880599235307907…48556673872609292001

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

1.479 × 10⁹⁷(98-digit number)

14796176119847061581…97113347745218583999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.479 × 10⁹⁷(98-digit number)

14796176119847061581…97113347745218584001

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

2.959 × 10⁹⁷(98-digit number)

29592352239694123163…94226695490437167999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.959 × 10⁹⁷(98-digit number)

29592352239694123163…94226695490437168001

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

5.918 × 10⁹⁷(98-digit number)

59184704479388246326…88453390980874335999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.918 × 10⁹⁷(98-digit number)

59184704479388246326…88453390980874336001

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

Block #386,644

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