Block #1,587,428

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/16/2016, 6:07:20 PM · Difficulty 10.6503 · 5,243,330 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fae723431ea8d7bd55c3fd863a026bfe72ab262161fda9e0d7b22cfa92be8b8e

View on Chainz ↗

Height

#1,587,428

Difficulty

10.650313

Transactions

Size

244 B

Version

Bits

0aa67ae7

Nonce

456,847,404

Timestamp

5/16/2016, 6:07:20 PM

Confirmations

5,243,330

Mined by

⛏️ P2SHAQXNNLgcayd35Wnn7J32SYrXmekBjowpEw

Merkle Root

c038423604e63b727adbca17396589bdebf1349ec851a2d8e538934d22fda56a

Transactions (1)

Coinbasec038423604e63b…38934d22fda56a

1 in → 2 out8.8000 XPM152 B

AQXNNLgc…kBjowpEw ALPu3s2c…EJXLjVFh

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.

2.429 × 10⁹⁸(99-digit number)

24294941984916028097…80789013069504389119

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

2.429 × 10⁹⁸(99-digit number)

24294941984916028097…80789013069504389119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.429 × 10⁹⁸(99-digit number)

24294941984916028097…80789013069504389121

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

4.858 × 10⁹⁸(99-digit number)

48589883969832056194…61578026139008778239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.858 × 10⁹⁸(99-digit number)

48589883969832056194…61578026139008778241

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

9.717 × 10⁹⁸(99-digit number)

97179767939664112389…23156052278017556479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.717 × 10⁹⁸(99-digit number)

97179767939664112389…23156052278017556481

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

1.943 × 10⁹⁹(100-digit number)

19435953587932822477…46312104556035112959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.943 × 10⁹⁹(100-digit number)

19435953587932822477…46312104556035112961

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

3.887 × 10⁹⁹(100-digit number)

38871907175865644955…92624209112070225919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.887 × 10⁹⁹(100-digit number)

38871907175865644955…92624209112070225921

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 #1,587,428

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