Block #2,057,422

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2017, 8:28:27 PM · Difficulty 10.8310 · 4,786,618 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

21fbcf69f3afa6d584a489d3f6444db2a23b363a85bf0dcc1cda3ad680be1e63

View on Chainz ↗

Height

#2,057,422

Difficulty

10.831003

Transactions

Size

1.14 KB

Version

Bits

0ad4bc9a

Nonce

385,925,530

Timestamp

4/5/2017, 8:28:27 PM

Confirmations

4,786,618

Mined by

⛏️ P2SHAPr7Neh2BMquNFUgCiDMHdmEV1zgZ2if6H

Merkle Root

ac27142be72f34c16c3a249a42d42702239ae45ac579c5995fe7567a3c27612f

Transactions (2)

Coinbase774e7fde1aa916…4508b10b6729bb

1 in → 1 out8.5200 XPM109 B

APr7Neh2…zgZ2if6H

cda9935e2b0d55…845e42756302dc

6 in → 2 out5817.5503 XPM968 B

Ada1dx2w…8gd1gZg2 AYhyPuWo…73G5mcGH

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.

7.799 × 10⁹⁵(96-digit number)

77994013704013506843…54622779481194495999

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

7.799 × 10⁹⁵(96-digit number)

77994013704013506843…54622779481194495999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.799 × 10⁹⁵(96-digit number)

77994013704013506843…54622779481194496001

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

1.559 × 10⁹⁶(97-digit number)

15598802740802701368…09245558962388991999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.559 × 10⁹⁶(97-digit number)

15598802740802701368…09245558962388992001

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

3.119 × 10⁹⁶(97-digit number)

31197605481605402737…18491117924777983999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.119 × 10⁹⁶(97-digit number)

31197605481605402737…18491117924777984001

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

6.239 × 10⁹⁶(97-digit number)

62395210963210805475…36982235849555967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.239 × 10⁹⁶(97-digit number)

62395210963210805475…36982235849555968001

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

1.247 × 10⁹⁷(98-digit number)

12479042192642161095…73964471699111935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.247 × 10⁹⁷(98-digit number)

12479042192642161095…73964471699111936001

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 #2,057,422

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