Block #470,557

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/1/2014, 11:56:19 PM · Difficulty 10.4317 · 6,355,740 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bb1db1f22daf5cc4b9e9247a5fac36ad8d01ef7f5a7abf0db4c5bff41b1a29a9

View on Chainz ↗

Height

#470,557

Difficulty

10.431687

Transactions

Size

1.25 KB

Version

Bits

0a6e8302

Nonce

34,910,326

Timestamp

4/1/2014, 11:56:19 PM

Confirmations

6,355,740

Mined by

⛏️ P2SHAWVQQcF6Rf3cW6oU9sfLA13fogreV8sPpV

Merkle Root

71ca3dfef660feae1b3b230d636ba253b7f1fff0b2ca24813b17c0a5e761217d

Transactions (4)

Coinbase116630855d3357…1842163859f7ab

1 in → 1 out9.2100 XPM109 B

AWVQQcF6…reV8sPpV

47f2fbc1d4e1e6…053a91463bd74f

3 in → 6 out15.5336 XPM625 B

AXA2CgAY…sjcwKJeP AL9UZuKj…g3Q3eciV AeotpmGC…wXWBzvh3 AeKNrjNj…1NEq95Ta Ab1YTAY5…9zZqa2sB

c3ff4334f40e23…eb077d77c05f9d

1 in → 2 out8.1458 XPM226 B

AZNTC7RQ…kQoB9YdW AFrB2KiU…sqy4Coqk

1e5aab1c237771…39c6f7edcfe7f0

1 in → 2 out6.1251 XPM226 B

AUfjwZDA…zKqSmaRQ AGAuDbuA…ed3nVPFw

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.

1.589 × 10⁹⁶(97-digit number)

15895749910279514815…36105915487312568319

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

1.589 × 10⁹⁶(97-digit number)

15895749910279514815…36105915487312568319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.589 × 10⁹⁶(97-digit number)

15895749910279514815…36105915487312568321

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

3.179 × 10⁹⁶(97-digit number)

31791499820559029630…72211830974625136639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.179 × 10⁹⁶(97-digit number)

31791499820559029630…72211830974625136641

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

6.358 × 10⁹⁶(97-digit number)

63582999641118059260…44423661949250273279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.358 × 10⁹⁶(97-digit number)

63582999641118059260…44423661949250273281

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

1.271 × 10⁹⁷(98-digit number)

12716599928223611852…88847323898500546559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.271 × 10⁹⁷(98-digit number)

12716599928223611852…88847323898500546561

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

2.543 × 10⁹⁷(98-digit number)

25433199856447223704…77694647797001093119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.543 × 10⁹⁷(98-digit number)

25433199856447223704…77694647797001093121

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 #470,557

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