Block #390,989

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/5/2014, 12:56:58 PM · Difficulty 10.4261 · 6,412,721 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5122b04dc70452b7bd4906b119dddf73fa560c9d4da746a20406c67638c667e2

View on Chainz ↗

Height

#390,989

Difficulty

10.426146

Transactions

Size

2.34 KB

Version

Bits

0a6d17e3

Nonce

95,460

Timestamp

2/5/2014, 12:56:58 PM

Confirmations

6,412,721

Mined by

⛏️ MaR46AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c2a6b20d87287c16c225c170eac7f4dd2049ca4aaffcff938275caa2dcb81198

Transactions (4)

Coinbasee89445201c63d5…b1c1a7bdd68e72

1 in → 20 out9.1900 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

7338acbfde861d…9f62773ac0e05c

1 in → 2 out1.0101 XPM226 B

AefxCEKS…AFgRpxyy AL7idMP1…tzVvoRrw

30895ff5f2f65c…1558e79587ff86

6 in → 2 out18.2843 XPM966 B

AbfNvWGE…B6PJ4amX AJbciRnE…f3xz4ckQ

edb7cc03f4a49f…91a559ff95026d

2 in → 2 out1.1304 XPM373 B

AeAEUcRK…fNfhusYR AJz987nj…X2bMmzq6

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.

6.553 × 10⁹⁶(97-digit number)

65537626213630451508…10122864935711457449

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

6.553 × 10⁹⁶(97-digit number)

65537626213630451508…10122864935711457449

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.553 × 10⁹⁶(97-digit number)

65537626213630451508…10122864935711457451

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

1.310 × 10⁹⁷(98-digit number)

13107525242726090301…20245729871422914899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.310 × 10⁹⁷(98-digit number)

13107525242726090301…20245729871422914901

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

2.621 × 10⁹⁷(98-digit number)

26215050485452180603…40491459742845829799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.621 × 10⁹⁷(98-digit number)

26215050485452180603…40491459742845829801

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

5.243 × 10⁹⁷(98-digit number)

52430100970904361206…80982919485691659599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.243 × 10⁹⁷(98-digit number)

52430100970904361206…80982919485691659601

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

1.048 × 10⁹⁸(99-digit number)

10486020194180872241…61965838971383319199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.048 × 10⁹⁸(99-digit number)

10486020194180872241…61965838971383319201

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

2.097 × 10⁹⁸(99-digit number)

20972040388361744482…23931677942766638399

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