Block #454,269

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/21/2014, 7:54:55 PM · Difficulty 10.3982 · 6,353,806 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2d8a543f2867b69f430263eea99b13fd102d7192905f906152c169c02b9f1807

View on Chainz ↗

Height

#454,269

Difficulty

10.398161

Transactions

Size

1.23 KB

Version

Bits

0a65ede5

Nonce

263,701

Timestamp

3/21/2014, 7:54:55 PM

Confirmations

6,353,806

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5ed4d4939426c0a36a921ccc1b6d0d061e726291b3dfc745900d3313dc99d6f9

Transactions (2)

Coinbase17fced777caf40…b59a6c639f1fc8

1 in → 1 out9.2500 XPM116 B

AbwWkWZt…kawDhufa

3bcad84669fd9f…865c1aec4e3a6d

5 in → 13 out39.3006 XPM1.03 KB

Acq7Tfk5…5zvD82s5 AVb4Tt4v…3Ze2LZ5q AUdGkUjR…APKVeDEY ALG6Kwki…JVRCDqef AdjVuW2o…RiqZiW4R

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.

3.531 × 10⁹⁶(97-digit number)

35318120502085080432…36887720325382750719

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

3.531 × 10⁹⁶(97-digit number)

35318120502085080432…36887720325382750719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.531 × 10⁹⁶(97-digit number)

35318120502085080432…36887720325382750721

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

7.063 × 10⁹⁶(97-digit number)

70636241004170160864…73775440650765501439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.063 × 10⁹⁶(97-digit number)

70636241004170160864…73775440650765501441

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

1.412 × 10⁹⁷(98-digit number)

14127248200834032172…47550881301531002879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.412 × 10⁹⁷(98-digit number)

14127248200834032172…47550881301531002881

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

2.825 × 10⁹⁷(98-digit number)

28254496401668064345…95101762603062005759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.825 × 10⁹⁷(98-digit number)

28254496401668064345…95101762603062005761

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

5.650 × 10⁹⁷(98-digit number)

56508992803336128691…90203525206124011519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.650 × 10⁹⁷(98-digit number)

56508992803336128691…90203525206124011521

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 #454,269

Cookie Preferences