Block #451,143

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/19/2014, 5:42:59 PM · Difficulty 10.3823 · 6,365,508 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2c30e39ade00893a1a0ce45ca74ff265e0aa6084b9669ea5a77c2420a4998dc5

View on Chainz ↗

Height

#451,143

Difficulty

10.382301

Transactions

Size

425 B

Version

Bits

0a61de74

Nonce

279,911

Timestamp

3/19/2014, 5:42:59 PM

Confirmations

6,365,508

Mined by

⛏️ P2SHAcH2s7Y4D9hVCSQQdA7jo9e2ue1nk8yDe6

Merkle Root

d205f88fb528298256a8c3afa2f27678fa6684b2b1527b624a116d4c656912cc

Transactions (2)

Coinbase27538edfc8e0cf…ea6a0c29fabfe3

1 in → 1 out9.2700 XPM109 B

AcH2s7Y4…1nk8yDe6

c5068008137af7…8660376e0d164e

1 in → 2 out54.6342 XPM225 B

AaHMfqkv…3A9sBEpv AUyccTTx…Ajknscro

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.

4.990 × 10⁹⁷(98-digit number)

49908358139193066134…71861534965918812159

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

4.990 × 10⁹⁷(98-digit number)

49908358139193066134…71861534965918812159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.990 × 10⁹⁷(98-digit number)

49908358139193066134…71861534965918812161

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

9.981 × 10⁹⁷(98-digit number)

99816716278386132269…43723069931837624319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.981 × 10⁹⁷(98-digit number)

99816716278386132269…43723069931837624321

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

1.996 × 10⁹⁸(99-digit number)

19963343255677226453…87446139863675248639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.996 × 10⁹⁸(99-digit number)

19963343255677226453…87446139863675248641

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

3.992 × 10⁹⁸(99-digit number)

39926686511354452907…74892279727350497279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.992 × 10⁹⁸(99-digit number)

39926686511354452907…74892279727350497281

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

7.985 × 10⁹⁸(99-digit number)

79853373022708905815…49784559454700994559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.985 × 10⁹⁸(99-digit number)

79853373022708905815…49784559454700994561

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 #451,143

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