Block #254,639

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 8:03:50 PM · Difficulty 9.9734 · 6,551,536 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ae2d2decf943c5041188b5430d70ef7d8d709896f08bf0b1a976a6c9717ad0f4

View on Chainz ↗

Height

#254,639

Difficulty

9.973391

Transactions

Size

685 B

Version

Bits

09f93025

Nonce

13,110

Timestamp

11/10/2013, 8:03:50 PM

Confirmations

6,551,536

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

b1127d32933d075607b5bdd45de75b44ff33fa4d59a48b994bbca83f8dffe86d

Transactions (3)

Coinbase48213fe7a4ef55…c67e0818f06426

1 in → 2 out10.0600 XPM142 B

AdGRRh1e…QmctLb24 ALfEGCwh…VawujfMm

aac8c566b4d06e…b894d1f89831ce

1 in → 2 out10.0400 XPM226 B

AaHs6RhP…qHhSSk3c AN3QK9wE…SHQv3wVg

b8459c3b278220…fb6f8456f5d4ba

1 in → 2 out4.9872 XPM226 B

ARxMsjSc…dpyj1eyf ASyL3JZF…2Mf9V5tj

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.

3.295 × 10⁹⁷(98-digit number)

32957550388033602609…27353576121571910399

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

3.295 × 10⁹⁷(98-digit number)

32957550388033602609…27353576121571910399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.295 × 10⁹⁷(98-digit number)

32957550388033602609…27353576121571910401

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

6.591 × 10⁹⁷(98-digit number)

65915100776067205218…54707152243143820799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.591 × 10⁹⁷(98-digit number)

65915100776067205218…54707152243143820801

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

1.318 × 10⁹⁸(99-digit number)

13183020155213441043…09414304486287641599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.318 × 10⁹⁸(99-digit number)

13183020155213441043…09414304486287641601

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

2.636 × 10⁹⁸(99-digit number)

26366040310426882087…18828608972575283199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.636 × 10⁹⁸(99-digit number)

26366040310426882087…18828608972575283201

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

5.273 × 10⁹⁸(99-digit number)

52732080620853764174…37657217945150566399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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