Block #1,420,880

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2016, 6:08:14 AM · Difficulty 10.7886 · 5,420,228 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8684c87c0d847f18d712eb2d8f1bfc5e68f978ad138c4aa9778b3f383fc19e2e

View on Chainz ↗

Height

#1,420,880

Difficulty

10.788590

Transactions

Size

1.22 KB

Version

Bits

0ac9e101

Nonce

314,121,769

Timestamp

1/20/2016, 6:08:14 AM

Confirmations

5,420,228

Mined by

⛏️ P2SHAe2d3d243skfoTXas3cvj8fKQJWLPLUZPV

Merkle Root

c4b741f66691ba2971757adc281074f7cadbf21a1e34b18cffdbcec151a5f57f

Transactions (3)

Coinbasef9894a2df9d560…841c3fed895942

1 in → 1 out8.6000 XPM109 B

Ae2d3d24…WLPLUZPV

9106f29437dc91…9e1534a72eb1d9

3 in → 1 out99.9900 XPM488 B

AWpaCrjZ…jTKttayh

a52ef6b3f3400d…3460acb82a196e

1 in → 12 out10.3519 XPM565 B

ASNueevd…k51oyWvn AXLkjH6Q…9wXKhR9V AWKEBBRp…3n9hJMog ATHiAJej…tjruF49b ATyHFdjS…kku74cEm

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.

2.111 × 10⁹⁷(98-digit number)

21110520967764748846…95435339323705917439

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

2.111 × 10⁹⁷(98-digit number)

21110520967764748846…95435339323705917439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.111 × 10⁹⁷(98-digit number)

21110520967764748846…95435339323705917441

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

4.222 × 10⁹⁷(98-digit number)

42221041935529497693…90870678647411834879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.222 × 10⁹⁷(98-digit number)

42221041935529497693…90870678647411834881

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

8.444 × 10⁹⁷(98-digit number)

84442083871058995387…81741357294823669759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.444 × 10⁹⁷(98-digit number)

84442083871058995387…81741357294823669761

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

1.688 × 10⁹⁸(99-digit number)

16888416774211799077…63482714589647339519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.688 × 10⁹⁸(99-digit number)

16888416774211799077…63482714589647339521

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

3.377 × 10⁹⁸(99-digit number)

33776833548423598155…26965429179294679039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.377 × 10⁹⁸(99-digit number)

33776833548423598155…26965429179294679041

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 #1,420,880

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