Block #450,955

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/19/2014, 2:41:45 PM · Difficulty 10.3810 · 6,357,108 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

75b678d7c621aa2c74ed2a8cc40631308fcea002fbe2e94b74e67922ff8384ce

View on Chainz ↗

Height

#450,955

Difficulty

10.381018

Transactions

Size

4.53 KB

Version

Bits

0a618a63

Nonce

57,162

Timestamp

3/19/2014, 2:41:45 PM

Confirmations

6,357,108

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c9c9e9c89bbe9db9de358ad2cfc26c3edbf86160eea2fddbf7a551c4d759a68f

Transactions (2)

Coinbasef0a9cc4c1ef5a1…0b75f87ee46909

1 in → 1 out9.3200 XPM110 B

AeKNrjNj…1NEq95Ta

8c5bb364c57ddc…791519010cdd11

17 in → 56 out158.1300 XPM4.33 KB

Af1Eejkx…cKmYn3YE Aepo3mhd…AwoPnjG3 APQCLq5D…cpNbYpoy AUkdqaxr…4jcbMUQ7 APSoHXZY…kNZx697r

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.

7.136 × 10⁹⁵(96-digit number)

71365537334448667399…19704668544222075519

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

7.136 × 10⁹⁵(96-digit number)

71365537334448667399…19704668544222075519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.136 × 10⁹⁵(96-digit number)

71365537334448667399…19704668544222075521

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

1.427 × 10⁹⁶(97-digit number)

14273107466889733479…39409337088444151039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.427 × 10⁹⁶(97-digit number)

14273107466889733479…39409337088444151041

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

2.854 × 10⁹⁶(97-digit number)

28546214933779466959…78818674176888302079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.854 × 10⁹⁶(97-digit number)

28546214933779466959…78818674176888302081

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

5.709 × 10⁹⁶(97-digit number)

57092429867558933919…57637348353776604159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.709 × 10⁹⁶(97-digit number)

57092429867558933919…57637348353776604161

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

1.141 × 10⁹⁷(98-digit number)

11418485973511786783…15274696707553208319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.141 × 10⁹⁷(98-digit number)

11418485973511786783…15274696707553208321

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 #450,955

Cookie Preferences