Block #456,107

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/23/2014, 12:06:16 AM · Difficulty 10.4165 · 6,361,906 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1a2afb956c754ce441c69f03198131d2bb632192f2fffa84fd7ff787622f8485

View on Chainz ↗

Height

#456,107

Difficulty

10.416525

Transactions

Size

1.01 KB

Version

Bits

0a6aa169

Nonce

23,560

Timestamp

3/23/2014, 12:06:16 AM

Confirmations

6,361,906

Mined by

⛏️ aS.%MAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

48a7ebb9b587bb5dd0a19856a254d88c5942a38293c75cf7be23cc9e9829989c

Transactions (1)

Coinbase48a7ebb9b587bb…23cc9e9829989c

1 in → 26 out9.2000 XPM947 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq

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.

9.212 × 10⁹³(94-digit number)

92129679520361636229…73384292647492342439

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

9.212 × 10⁹³(94-digit number)

92129679520361636229…73384292647492342439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.212 × 10⁹³(94-digit number)

92129679520361636229…73384292647492342441

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

1.842 × 10⁹⁴(95-digit number)

18425935904072327245…46768585294984684879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.842 × 10⁹⁴(95-digit number)

18425935904072327245…46768585294984684881

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

3.685 × 10⁹⁴(95-digit number)

36851871808144654491…93537170589969369759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.685 × 10⁹⁴(95-digit number)

36851871808144654491…93537170589969369761

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

7.370 × 10⁹⁴(95-digit number)

73703743616289308983…87074341179938739519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.370 × 10⁹⁴(95-digit number)

73703743616289308983…87074341179938739521

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

1.474 × 10⁹⁵(96-digit number)

14740748723257861796…74148682359877479039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.474 × 10⁹⁵(96-digit number)

14740748723257861796…74148682359877479041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.948 × 10⁹⁵(96-digit number)

29481497446515723593…48297364719754958079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #456,107

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