Block #2,192,340

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/4/2017, 8:06:12 AM · Difficulty 10.9513 · 4,634,770 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c8483509a5039b41195a8673fbc3139f63802d3ff6b3fb1f8776e02f9119c1f8

View on Chainz ↗

Height

#2,192,340

Difficulty

10.951347

Transactions

Size

1.86 KB

Version

Bits

0af38b78

Nonce

24,493,509

Timestamp

7/4/2017, 8:06:12 AM

Confirmations

4,634,770

Mined by

⛏️ P2SHAGq2fhLECWn5uY9x8uE5vgu41QWEdErEdg

Merkle Root

cf11799e7165e6a0d17d2283f62b7f441246c8fb7977f715e4f3723c4c3ec4bc

Transactions (2)

Coinbase1188bfae517d55…976b06c55092aa

1 in → 1 out8.3400 XPM110 B

AGq2fhLE…WEdErEdg

ed9a6d26707fd2…53577fa032112f

11 in → 2 out108.1642 XPM1.67 KB

Ab5Q3KF4…hBZkR1Di AHJeiJjZ…AtVjQXra

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.

1.005 × 10⁹⁷(98-digit number)

10054882869076524332…97128493107652254719

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

1.005 × 10⁹⁷(98-digit number)

10054882869076524332…97128493107652254719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.005 × 10⁹⁷(98-digit number)

10054882869076524332…97128493107652254721

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

2.010 × 10⁹⁷(98-digit number)

20109765738153048665…94256986215304509439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.010 × 10⁹⁷(98-digit number)

20109765738153048665…94256986215304509441

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

4.021 × 10⁹⁷(98-digit number)

40219531476306097330…88513972430609018879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.021 × 10⁹⁷(98-digit number)

40219531476306097330…88513972430609018881

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

8.043 × 10⁹⁷(98-digit number)

80439062952612194660…77027944861218037759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.043 × 10⁹⁷(98-digit number)

80439062952612194660…77027944861218037761

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

1.608 × 10⁹⁸(99-digit number)

16087812590522438932…54055889722436075519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.608 × 10⁹⁸(99-digit number)

16087812590522438932…54055889722436075521

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

3.217 × 10⁹⁸(99-digit number)

32175625181044877864…08111779444872151039

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 #2,192,340

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