Block #1,470,704

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/24/2016, 8:06:48 PM · Difficulty 10.7224 · 5,371,884 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

48577bb7084ab06fccf60c7085cc5e7f491ea6576e345292e2ee7827fb59d85e

View on Chainz ↗

Height

#1,470,704

Difficulty

10.722404

Transactions

Size

1.31 KB

Version

Bits

0ab8ef70

Nonce

1,243,473,387

Timestamp

2/24/2016, 8:06:48 PM

Confirmations

5,371,884

Mined by

⛏️ P2SHAKoMBt7zsdfWPFc57eXgdFgKtUfx1ENscB

Merkle Root

b6b95c69aab47acc40c7db526bbc0a947610e503d06f8194ee8ceccc962b20fb

Transactions (2)

Coinbasea2931f0d32b7fe…458dd77f432ca0

1 in → 1 out8.7000 XPM109 B

AKoMBt7z…fx1ENscB

86a6081e1a41cc…405c7aea1158c7

1 in → 29 out67.0071 XPM1.12 KB

AMKGtgoh…WjT1Tjsk AT8Q8XkZ…iNDFmx8z AY3hiCAM…iXMnBNhE AV8fBX7h…rcCJLHsu AP964WgM…L2oX7Eow

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.

2.314 × 10⁹⁴(95-digit number)

23145617385460602681…22514882123120284089

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

2.314 × 10⁹⁴(95-digit number)

23145617385460602681…22514882123120284089

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.314 × 10⁹⁴(95-digit number)

23145617385460602681…22514882123120284091

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

4.629 × 10⁹⁴(95-digit number)

46291234770921205362…45029764246240568179

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.629 × 10⁹⁴(95-digit number)

46291234770921205362…45029764246240568181

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

9.258 × 10⁹⁴(95-digit number)

92582469541842410724…90059528492481136359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.258 × 10⁹⁴(95-digit number)

92582469541842410724…90059528492481136361

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

1.851 × 10⁹⁵(96-digit number)

18516493908368482144…80119056984962272719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.851 × 10⁹⁵(96-digit number)

18516493908368482144…80119056984962272721

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

3.703 × 10⁹⁵(96-digit number)

37032987816736964289…60238113969924545439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.703 × 10⁹⁵(96-digit number)

37032987816736964289…60238113969924545441

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 #1,470,704

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