Block #549,470

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/17/2014, 2:12:37 PM · Difficulty 10.9608 · 6,267,707 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3519996a84e2bfed7036e7d36c4bf5a671dce95b98c3180f349336ccc012577d

View on Chainz ↗

Height

#549,470

Difficulty

10.960794

Transactions

Size

1.30 KB

Version

Bits

0af5f69a

Nonce

228,863,891

Timestamp

5/17/2014, 2:12:37 PM

Confirmations

6,267,707

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

df336a7c8f24afb30cfd62e35d35f7fe5158f42d3fa9c42ccbc3289f8ce3a738

Transactions (4)

Coinbasee0e0f957df8772…f8b3054f64c850

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

2061df57db0746…b95e8c10df0515

3 in → 2 out51.1363 XPM525 B

AHMvkrf7…Ej3xXp3R AUVkd2Ms…TRR9q9LV

9b634406233737…7bc6a938df77eb

2 in → 2 out14.4990 XPM373 B

AVaLFZ9k…qWX1KmjU AUbyCZmt…6VCxqEU1

a811dc134288de…607d9afc4174ec

1 in → 2 out1.4604 XPM226 B

AL4RdTaL…RQtoEqnD AdLTuBHb…LAst4dsG

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.

1.061 × 10⁹⁸(99-digit number)

10611906476933710336…92306100973707819999

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

1.061 × 10⁹⁸(99-digit number)

10611906476933710336…92306100973707819999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.061 × 10⁹⁸(99-digit number)

10611906476933710336…92306100973707820001

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

2.122 × 10⁹⁸(99-digit number)

21223812953867420673…84612201947415639999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.122 × 10⁹⁸(99-digit number)

21223812953867420673…84612201947415640001

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

4.244 × 10⁹⁸(99-digit number)

42447625907734841346…69224403894831279999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.244 × 10⁹⁸(99-digit number)

42447625907734841346…69224403894831280001

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

8.489 × 10⁹⁸(99-digit number)

84895251815469682692…38448807789662559999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.489 × 10⁹⁸(99-digit number)

84895251815469682692…38448807789662560001

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

1.697 × 10⁹⁹(100-digit number)

16979050363093936538…76897615579325119999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.697 × 10⁹⁹(100-digit number)

16979050363093936538…76897615579325120001

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 #549,470

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