Block #420,193

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/26/2014, 5:38:40 AM · Difficulty 10.3675 · 6,377,928 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

197be94335c4502938dd61a8b2021dc84ea08a8b055bc23f132f1df826af31c6

View on Chainz ↗

Height

#420,193

Difficulty

10.367472

Transactions

Size

1.07 KB

Version

Bits

0a5e12ab

Nonce

67,599

Timestamp

2/26/2014, 5:38:40 AM

Confirmations

6,377,928

Mined by

⛏️ P2SHAWqmsKF4Az5JVLfaHGjHzooYoGePBxKA2f

Merkle Root

b5e1cc55b221ade139ab6c2c5f891e18356b57dfe5f378aba4d05ad3605498ca

Transactions (3)

Coinbase045808922906e4…8fe4a590ecdf36

1 in → 1 out9.3100 XPM109 B

AWqmsKF4…ePBxKA2f

cb1b6045ff7f37…a483d32f5e3231

4 in → 2 out3.0126 XPM671 B

AMvgAGw9…S77EDqE5 APrypsuZ…5qF56X11

2069e19ad4f772…d0614aa15d7da8

1 in → 2 out1.0753 XPM227 B

AGxMeQpn…PtE4vAxN ATdyvnUZ…p1Kxc8S9

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.

5.335 × 10⁹⁶(97-digit number)

53354086901288462172…30914832578470719669

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

5.335 × 10⁹⁶(97-digit number)

53354086901288462172…30914832578470719669

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.335 × 10⁹⁶(97-digit number)

53354086901288462172…30914832578470719671

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

1.067 × 10⁹⁷(98-digit number)

10670817380257692434…61829665156941439339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.067 × 10⁹⁷(98-digit number)

10670817380257692434…61829665156941439341

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

2.134 × 10⁹⁷(98-digit number)

21341634760515384869…23659330313882878679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.134 × 10⁹⁷(98-digit number)

21341634760515384869…23659330313882878681

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

4.268 × 10⁹⁷(98-digit number)

42683269521030769738…47318660627765757359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.268 × 10⁹⁷(98-digit number)

42683269521030769738…47318660627765757361

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

8.536 × 10⁹⁷(98-digit number)

85366539042061539476…94637321255531514719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.536 × 10⁹⁷(98-digit number)

85366539042061539476…94637321255531514721

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