Block #1,687,459

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/24/2016, 3:07:05 PM · Difficulty 10.7083 · 5,143,217 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b66a6ab2d16e3ed5f9e302d70c32ea8c8e4deb7deefd5b93e61792127a2c3e3

View on Chainz ↗

Height

#1,687,459

Difficulty

10.708325

Transactions

Size

1018 B

Version

Bits

0ab554c9

Nonce

100,194,194

Timestamp

7/24/2016, 3:07:05 PM

Confirmations

5,143,217

Mined by

⛏️ P2SHAWsixSMR2SkM9h3tAZpc2FbZenZCzy1ApA

Merkle Root

34e2cc9201384ab348daa6fb1fa228c4f8d926d8828ac6e67a00cefcf9adb98b

Transactions (2)

Coinbase9d90aad32e0cd8…54e41b39932aea

1 in → 1 out8.7200 XPM109 B

AWsixSMR…ZCzy1ApA

3ff8b3080ff7c5…a9ac4a5e987d9c

5 in → 2 out60.8127 XPM817 B

APoeWgEU…g9RgLt3G AQcjeddP…AoqhXrhG

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.

3.327 × 10⁹⁸(99-digit number)

33276232932521673885…58010785831754465279

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

3.327 × 10⁹⁸(99-digit number)

33276232932521673885…58010785831754465279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.327 × 10⁹⁸(99-digit number)

33276232932521673885…58010785831754465281

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

6.655 × 10⁹⁸(99-digit number)

66552465865043347770…16021571663508930559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.655 × 10⁹⁸(99-digit number)

66552465865043347770…16021571663508930561

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

1.331 × 10⁹⁹(100-digit number)

13310493173008669554…32043143327017861119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.331 × 10⁹⁹(100-digit number)

13310493173008669554…32043143327017861121

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

2.662 × 10⁹⁹(100-digit number)

26620986346017339108…64086286654035722239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.662 × 10⁹⁹(100-digit number)

26620986346017339108…64086286654035722241

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

5.324 × 10⁹⁹(100-digit number)

53241972692034678216…28172573308071444479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.324 × 10⁹⁹(100-digit number)

53241972692034678216…28172573308071444481

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

1.064 × 10¹⁰⁰(101-digit number)

10648394538406935643…56345146616142888959

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 #1,687,459

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