Block #1,430,726

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/27/2016, 1:05:21 PM · Difficulty 10.7598 · 5,385,480 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0b0263b15a9bd06e8d13b9f76d4e6f37bc17e5ba7b5e5f974654dfead97d9294

View on Chainz ↗

Height

#1,430,726

Difficulty

10.759791

Transactions

Size

629 B

Version

Bits

0ac281ab

Nonce

1,454,678,385

Timestamp

1/27/2016, 1:05:21 PM

Confirmations

5,385,480

Mined by

⛏️ P2SHAK8u9PfMPMnNCLWojZ5uYCbbBKM3bjSwcn

Merkle Root

be9eb3b6037d24e230bb3c48fe9fe12d7237105b4635af1e14a83a3d814aa6e2

Transactions (2)

Coinbase61d35624ebc2af…cd1473f3cd2b0e

1 in → 1 out8.6300 XPM110 B

AK8u9PfM…M3bjSwcn

0e035609a3215b…1e8166b5c5ba1d

1 in → 8 out184.3750 XPM429 B

APP5tctX…gsDaJjj9 AcCoJQto…PuCYg79o AHMNBwcx…yryAriBK AahNe9Eb…j7WvUkU7 Ac2aFd5d…aMXhNyZn

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.

2.341 × 10⁹⁴(95-digit number)

23416092597093959297…67706387149368000359

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

2.341 × 10⁹⁴(95-digit number)

23416092597093959297…67706387149368000359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.341 × 10⁹⁴(95-digit number)

23416092597093959297…67706387149368000361

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

4.683 × 10⁹⁴(95-digit number)

46832185194187918594…35412774298736000719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.683 × 10⁹⁴(95-digit number)

46832185194187918594…35412774298736000721

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

9.366 × 10⁹⁴(95-digit number)

93664370388375837188…70825548597472001439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.366 × 10⁹⁴(95-digit number)

93664370388375837188…70825548597472001441

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

1.873 × 10⁹⁵(96-digit number)

18732874077675167437…41651097194944002879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.873 × 10⁹⁵(96-digit number)

18732874077675167437…41651097194944002881

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

3.746 × 10⁹⁵(96-digit number)

37465748155350334875…83302194389888005759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.746 × 10⁹⁵(96-digit number)

37465748155350334875…83302194389888005761

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

7.493 × 10⁹⁵(96-digit number)

74931496310700669750…66604388779776011519

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 #1,430,726

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