Block #464,431

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2014, 6:53:49 PM · Difficulty 10.4215 · 6,343,362 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

29521ab035e2a134f1aa0fc41f1d7d8540cefd5f3241cae30358c3cb3824058e

View on Chainz ↗

Height

#464,431

Difficulty

10.421530

Transactions

Size

878 B

Version

Bits

0a6be95f

Nonce

119,568

Timestamp

3/28/2014, 6:53:49 PM

Confirmations

6,343,362

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

8d1bd8849b7578aa44ffa1dafc2e8080d65ceaba02463feb8c843d4884cb0ec3

Transactions (4)

Coinbase6779376c07a752…c5d3b7d51fb73a

1 in → 1 out9.2200 XPM110 B

AeKNrjNj…1NEq95Ta

4b2c568f02d32d…df783e5f569769

1 in → 2 out7.1639 XPM226 B

AeDFWfLr…ocqM5DJT AVLedgvg…9aqjVjZh

2d641682f2339e…585dd9bf4ffdc1

1 in → 2 out6.1475 XPM226 B

AUfZq9jz…xEGBvByx AVwWPpAT…j8nd7haB

ba46ea8c173682…62ffb0e9ebbf90

1 in → 2 out3.6051 XPM226 B

AMZrLEPg…TBFEHRTa APFsQ3Fo…xoFKrF12

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.

2.963 × 10⁹⁵(96-digit number)

29631163077127512845…80441935624825360419

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

2.963 × 10⁹⁵(96-digit number)

29631163077127512845…80441935624825360419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.963 × 10⁹⁵(96-digit number)

29631163077127512845…80441935624825360421

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

5.926 × 10⁹⁵(96-digit number)

59262326154255025691…60883871249650720839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.926 × 10⁹⁵(96-digit number)

59262326154255025691…60883871249650720841

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

1.185 × 10⁹⁶(97-digit number)

11852465230851005138…21767742499301441679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.185 × 10⁹⁶(97-digit number)

11852465230851005138…21767742499301441681

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

2.370 × 10⁹⁶(97-digit number)

23704930461702010276…43535484998602883359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.370 × 10⁹⁶(97-digit number)

23704930461702010276…43535484998602883361

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

4.740 × 10⁹⁶(97-digit number)

47409860923404020553…87070969997205766719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.740 × 10⁹⁶(97-digit number)

47409860923404020553…87070969997205766721

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 #464,431

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