Block #1,481,928

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/3/2016, 2:08:38 PM · Difficulty 10.7261 · 5,351,640 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0356804a1196bdc4f202fcc20d4b799e11bf32b13d88271760975240986c2d4

View on Chainz ↗

Height

#1,481,928

Difficulty

10.726065

Transactions

Size

970 B

Version

Bits

0ab9df6b

Nonce

656,227,986

Timestamp

3/3/2016, 2:08:38 PM

Confirmations

5,351,640

Mined by

⛏️ P2SHAYLFLAnWT5TNd4defxUFy7Smw888wmTgCY

Merkle Root

bf5c046a4d79a3b909f71b326aeb1951344a666b42643ff56e70ace81bb7dbf9

Transactions (2)

Coinbase9fc4bd5c2ac46a…e97c801e2de7bf

1 in → 1 out8.6900 XPM109 B

AYLFLAnW…88wmTgCY

74d258bb7df505…2c9b547d9ef0a6

1 in → 18 out152.6395 XPM770 B

AL3GJHVD…1jrz8AHJ AMTjygiN…v9bhs1QX AJdhtvrL…F9wUA9XE AYXTz78e…RfsWmrAH AYSS7wNK…KgMX99y4

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.

2.230 × 10⁹⁷(98-digit number)

22308100801041911655…29830580226660208639

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

2.230 × 10⁹⁷(98-digit number)

22308100801041911655…29830580226660208639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.230 × 10⁹⁷(98-digit number)

22308100801041911655…29830580226660208641

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

4.461 × 10⁹⁷(98-digit number)

44616201602083823311…59661160453320417279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.461 × 10⁹⁷(98-digit number)

44616201602083823311…59661160453320417281

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

8.923 × 10⁹⁷(98-digit number)

89232403204167646623…19322320906640834559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.923 × 10⁹⁷(98-digit number)

89232403204167646623…19322320906640834561

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

1.784 × 10⁹⁸(99-digit number)

17846480640833529324…38644641813281669119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.784 × 10⁹⁸(99-digit number)

17846480640833529324…38644641813281669121

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

3.569 × 10⁹⁸(99-digit number)

35692961281667058649…77289283626563338239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.569 × 10⁹⁸(99-digit number)

35692961281667058649…77289283626563338241

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

7.138 × 10⁹⁸(99-digit number)

71385922563334117298…54578567253126676479

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 #1,481,928

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