Block #1,585,098

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/15/2016, 3:07:12 AM · Difficulty 10.6510 · 5,242,012 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e24efc8f9f97f5cc64754d1a9cd3da9bbbbd664165d1c6cc2114dcb5e96b560b

View on Chainz ↗

Height

#1,585,098

Difficulty

10.651011

Transactions

Size

799 B

Version

Bits

0aa6a8a0

Nonce

110,068,366

Timestamp

5/15/2016, 3:07:12 AM

Confirmations

5,242,012

Mined by

⛏️ TAGonqPyfrFvwmREXtr9SnySE9XCPqeNeAn

Merkle Root

14fb3505dac517195776e701c0ddd9fc94c3ebfd02323e3f3ea99b147e6474af

Transactions (2)

Coinbase2b5e41c8889d0f…f4b6572a014d9c

1 in → 1 out8.8100 XPM109 B

AGonqPyf…CPqeNeAn

cbd32ab45ae777…d3e3d6584adc13

1 in → 13 out70.2087 XPM599 B

AYcjCG5T…uaLDGbPV AZuqYMWK…rX6W4xGX AbfFXrJQ…tSVBFXxG AGgmACZS…tT3pPwfT Ac9HqP8y…nj4GmPmr

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.

2.072 × 10⁹⁶(97-digit number)

20729045516883098649…29691518805723566079

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

2.072 × 10⁹⁶(97-digit number)

20729045516883098649…29691518805723566079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.072 × 10⁹⁶(97-digit number)

20729045516883098649…29691518805723566081

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

4.145 × 10⁹⁶(97-digit number)

41458091033766197299…59383037611447132159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.145 × 10⁹⁶(97-digit number)

41458091033766197299…59383037611447132161

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

8.291 × 10⁹⁶(97-digit number)

82916182067532394598…18766075222894264319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.291 × 10⁹⁶(97-digit number)

82916182067532394598…18766075222894264321

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

1.658 × 10⁹⁷(98-digit number)

16583236413506478919…37532150445788528639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.658 × 10⁹⁷(98-digit number)

16583236413506478919…37532150445788528641

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

3.316 × 10⁹⁷(98-digit number)

33166472827012957839…75064300891577057279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.316 × 10⁹⁷(98-digit number)

33166472827012957839…75064300891577057281

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 #1,585,098

Cookie Preferences