Block #2,079,152

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/20/2017, 8:20:21 AM · Difficulty 10.8582 · 4,761,260 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

217c7585b363ded1cb6cb5c53ea9740c27f9e1136051ae51c931a527622ac1a8

View on Chainz ↗

Height

#2,079,152

Difficulty

10.858153

Transactions

Size

428 B

Version

Bits

0adbafea

Nonce

696,383,490

Timestamp

4/20/2017, 8:20:21 AM

Confirmations

4,761,260

Mined by

⛏️ P2SHAVVSJ1vxxPTjD221u6ZgNDzqcUNMt64Nw9

Merkle Root

76306808ebd19618fd310a3c148e7806f2a8588adee172f9f63b7873bd546622

Transactions (2)

Coinbasea6c18b12d8ad7a…52c498aaa2c6d4

1 in → 1 out8.4800 XPM110 B

AVVSJ1vx…NMt64Nw9

32c8eb95c96ac4…5e18ae97358165

1 in → 2 out132297.1604 XPM227 B

AcZsZafW…9WuZdEWd AV2pNZxY…dPooW7Mo

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.

2.511 × 10⁹⁶(97-digit number)

25116927593766608715…47062563437960069119

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

2.511 × 10⁹⁶(97-digit number)

25116927593766608715…47062563437960069119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.511 × 10⁹⁶(97-digit number)

25116927593766608715…47062563437960069121

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

5.023 × 10⁹⁶(97-digit number)

50233855187533217431…94125126875920138239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.023 × 10⁹⁶(97-digit number)

50233855187533217431…94125126875920138241

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

1.004 × 10⁹⁷(98-digit number)

10046771037506643486…88250253751840276479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.004 × 10⁹⁷(98-digit number)

10046771037506643486…88250253751840276481

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

2.009 × 10⁹⁷(98-digit number)

20093542075013286972…76500507503680552959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.009 × 10⁹⁷(98-digit number)

20093542075013286972…76500507503680552961

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

4.018 × 10⁹⁷(98-digit number)

40187084150026573945…53001015007361105919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.018 × 10⁹⁷(98-digit number)

40187084150026573945…53001015007361105921

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 #2,079,152

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