Block #1,479,952

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2016, 8:06:00 AM · Difficulty 10.7164 · 5,362,143 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a8d3a78dd9e9ae9546c8647a36cd05ef8e1c0acc2142186c747257fcee733b54

View on Chainz ↗

Height

#1,479,952

Difficulty

10.716374

Transactions

Size

1.18 KB

Version

Bits

0ab76442

Nonce

327,436,972

Timestamp

3/2/2016, 8:06:00 AM

Confirmations

5,362,143

Mined by

⛏️ P2SHAPJ6q8BLCYKxKdh5dDGju68XGuft5nHaSG

Merkle Root

1c4638ad94c7a08405f70ab63e55e082c8f1632f81003daab9817b29a783843d

Transactions (2)

Coinbasef615797547e1a2…6a0f92d3fe25f5

1 in → 1 out8.7100 XPM110 B

APJ6q8BL…ft5nHaSG

b99fc1c06cc9b4…40c1bcbc5958dd

1 in → 25 out180.0858 XPM1008 B

AMfZuhaw…gFDWTRSN AX2bQuJG…ha4XpsRn AbEDgMQW…1p5Rbhx4 AVdGiQFD…RS9pbsZA AKfvgRrx…8ofBH9ED

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.

1.375 × 10⁹⁷(98-digit number)

13753482031564320630…12317733122485800959

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

1.375 × 10⁹⁷(98-digit number)

13753482031564320630…12317733122485800959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.375 × 10⁹⁷(98-digit number)

13753482031564320630…12317733122485800961

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

2.750 × 10⁹⁷(98-digit number)

27506964063128641260…24635466244971601919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.750 × 10⁹⁷(98-digit number)

27506964063128641260…24635466244971601921

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

5.501 × 10⁹⁷(98-digit number)

55013928126257282520…49270932489943203839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.501 × 10⁹⁷(98-digit number)

55013928126257282520…49270932489943203841

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

1.100 × 10⁹⁸(99-digit number)

11002785625251456504…98541864979886407679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.100 × 10⁹⁸(99-digit number)

11002785625251456504…98541864979886407681

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

2.200 × 10⁹⁸(99-digit number)

22005571250502913008…97083729959772815359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.200 × 10⁹⁸(99-digit number)

22005571250502913008…97083729959772815361

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 #1,479,952

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