Block #1,598,625

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/24/2016, 9:59:44 PM · Difficulty 10.6102 · 5,213,621 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f9cf2cf290865e9050793d4095580d90265cf8e3edc01d56506adbc72efe9b73

View on Chainz ↗

Height

#1,598,625

Difficulty

10.610243

Transactions

Size

30.73 KB

Version

Bits

0a9c38dd

Nonce

464,340,898

Timestamp

5/24/2016, 9:59:44 PM

Confirmations

5,213,621

Mined by

⛏️ P2SHANfPphvidZVnJrgK4VYTuHai1CTGJLucV3

Merkle Root

060c874221010ef92407cc1df05ebc1bfecf83f4fcdc0b0074b8146a15b7fea2

Transactions (2)

Coinbase7c572daedda09c…ade4aee30a094e

1 in → 1 out9.1900 XPM109 B

ANfPphvi…TGJLucV3

aac9a897440345…0ffaa1120ac40b

211 in → 1 out492.1925 XPM30.54 KB

AJcE2yJy…7uEM8rVX

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.

1.171 × 10⁹¹(92-digit number)

11714852413895481779…73493149174079788619

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

1.171 × 10⁹¹(92-digit number)

11714852413895481779…73493149174079788619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.171 × 10⁹¹(92-digit number)

11714852413895481779…73493149174079788621

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

2.342 × 10⁹¹(92-digit number)

23429704827790963559…46986298348159577239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.342 × 10⁹¹(92-digit number)

23429704827790963559…46986298348159577241

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

4.685 × 10⁹¹(92-digit number)

46859409655581927119…93972596696319154479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.685 × 10⁹¹(92-digit number)

46859409655581927119…93972596696319154481

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

9.371 × 10⁹¹(92-digit number)

93718819311163854239…87945193392638308959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.371 × 10⁹¹(92-digit number)

93718819311163854239…87945193392638308961

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

1.874 × 10⁹²(93-digit number)

18743763862232770847…75890386785276617919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.874 × 10⁹²(93-digit number)

18743763862232770847…75890386785276617921

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 #1,598,625

Cookie Preferences