Block #1,420,735

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2016, 3:32:16 AM · Difficulty 10.7890 · 5,424,095 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b498680d62fdfbed68bf7bfad3ee62cfddc6f8c1e861bbf257c4d2f6f907fdb7

View on Chainz ↗

Height

#1,420,735

Difficulty

10.788971

Transactions

Size

425 B

Version

Bits

0ac9f9fd

Nonce

261,263,717

Timestamp

1/20/2016, 3:32:16 AM

Confirmations

5,424,095

Mined by

⛏️ P2SHAW3zEiRdCGqn94wQQEV5V8oeuUA87VHNh3

Merkle Root

6b2dd829bc8656b0d26bfb3892c4888f049b8051b9ac3096c36cd67380a9cc0c

Transactions (2)

Coinbase21b47e23415dc1…df12b88e90a1c6

1 in → 1 out8.5900 XPM110 B

AW3zEiRd…A87VHNh3

4f3641e3e6af8d…1b913a1ba15f1b

1 in → 2 out66.0450 XPM225 B

AavpDyjF…9Qcf8QNL AYjRofGY…FJ9YdQYv

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.

2.455 × 10⁹⁵(96-digit number)

24559353947221720365…27260690139133378559

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

2.455 × 10⁹⁵(96-digit number)

24559353947221720365…27260690139133378559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.455 × 10⁹⁵(96-digit number)

24559353947221720365…27260690139133378561

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

4.911 × 10⁹⁵(96-digit number)

49118707894443440730…54521380278266757119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.911 × 10⁹⁵(96-digit number)

49118707894443440730…54521380278266757121

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

9.823 × 10⁹⁵(96-digit number)

98237415788886881461…09042760556533514239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.823 × 10⁹⁵(96-digit number)

98237415788886881461…09042760556533514241

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

1.964 × 10⁹⁶(97-digit number)

19647483157777376292…18085521113067028479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.964 × 10⁹⁶(97-digit number)

19647483157777376292…18085521113067028481

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

3.929 × 10⁹⁶(97-digit number)

39294966315554752584…36171042226134056959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.929 × 10⁹⁶(97-digit number)

39294966315554752584…36171042226134056961

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 #1,420,735

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