Block #2,773,483

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/31/2018, 4:46:38 PM · Difficulty 11.6620 · 4,032,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0a0c2ef29b67aac439e968830d38e30d0989e7a6e6c2826bd354894204a1b4b7

View on Chainz ↗

Height

#2,773,483

Difficulty

11.662049

Transactions

Size

1.30 KB

Version

Bits

0ba97c10

Nonce

1,238,938,763

Timestamp

7/31/2018, 4:46:38 PM

Confirmations

4,032,832

Mined by

⛏️ P2SHAQx7WqoTdGSA1tZLZQKUvhwSaoJTt39XVu

Merkle Root

56f805a8818b4702604eb0d218e20a7512106aab6838bea6a7fb896f740a808d

Transactions (4)

Coinbasea5c131cbeebbe2…c9848efad923d7

1 in → 1 out7.3700 XPM110 B

AQx7WqoT…JTt39XVu

c312bfe35c01d6…6ff875e11b94ac

2 in → 2 out14.6900 XPM307 B

AQSBLSva…M7vP4jFk AXXGfizT…aeWx1Cui

e43ad39358d58f…b8a6fd5f283e07

2 in → 2 out12.0400 XPM340 B

AapXgA7m…gWZCRiEd AKD9LeNP…bQTn8mEf

0dfd122efa34c3…e636b88bcfaf19

3 in → 2 out10.7700 XPM488 B

AJLY5Acg…jPhrGPCW AM6XD26m…RcphfPC1

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.

4.868 × 10⁹⁷(98-digit number)

48689603548684341944…34731164499195985919

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

4.868 × 10⁹⁷(98-digit number)

48689603548684341944…34731164499195985919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.868 × 10⁹⁷(98-digit number)

48689603548684341944…34731164499195985921

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

9.737 × 10⁹⁷(98-digit number)

97379207097368683889…69462328998391971839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.737 × 10⁹⁷(98-digit number)

97379207097368683889…69462328998391971841

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

1.947 × 10⁹⁸(99-digit number)

19475841419473736777…38924657996783943679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.947 × 10⁹⁸(99-digit number)

19475841419473736777…38924657996783943681

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

3.895 × 10⁹⁸(99-digit number)

38951682838947473555…77849315993567887359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.895 × 10⁹⁸(99-digit number)

38951682838947473555…77849315993567887361

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

7.790 × 10⁹⁸(99-digit number)

77903365677894947111…55698631987135774719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.790 × 10⁹⁸(99-digit number)

77903365677894947111…55698631987135774721

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

1.558 × 10⁹⁹(100-digit number)

15580673135578989422…11397263974271549439

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

Block #2,773,483

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