Block #456,744

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 10:37:13 AM · Difficulty 10.4178 · 6,347,448 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

119dffcd65d1b50aaf0e8c429590e39b6a88da46d767725add49314b31e3b8df

View on Chainz ↗

Height

#456,744

Difficulty

10.417819

Transactions

Size

4.11 KB

Version

Bits

0a6af62a

Nonce

19,440

Timestamp

3/23/2014, 10:37:13 AM

Confirmations

6,347,448

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e897650d8c8792823148b80de84978c6ed889389da923a2af8e76946d5dc47e1

Transactions (3)

Coinbasedf44a2b705dfc0…785ddadf86eefa

1 in → 1 out9.2559 XPM110 B

AeKNrjNj…1NEq95Ta

4cb28958425922…7ccf1dc05b68cb

1 in → 4 out9.2500 XPM259 B

AG9iD1vm…aFxZeVd6 AeKNrjNj…1NEq95Ta AWppzrSM…CxCJ4whA AXHFnvkB…yXdZX2Fh

626091d0783e2b…c4759e4630bb0c

25 in → 1 out42.1000 XPM3.66 KB

AUztoXmf…nc7FN4za

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.

6.406 × 10¹⁰¹(102-digit number)

64060838794178891551…50128885801267427199

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

6.406 × 10¹⁰¹(102-digit number)

64060838794178891551…50128885801267427199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.406 × 10¹⁰¹(102-digit number)

64060838794178891551…50128885801267427201

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

1.281 × 10¹⁰²(103-digit number)

12812167758835778310…00257771602534854399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.281 × 10¹⁰²(103-digit number)

12812167758835778310…00257771602534854401

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

2.562 × 10¹⁰²(103-digit number)

25624335517671556620…00515543205069708799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.562 × 10¹⁰²(103-digit number)

25624335517671556620…00515543205069708801

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

5.124 × 10¹⁰²(103-digit number)

51248671035343113240…01031086410139417599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.124 × 10¹⁰²(103-digit number)

51248671035343113240…01031086410139417601

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

1.024 × 10¹⁰³(104-digit number)

10249734207068622648…02062172820278835199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.024 × 10¹⁰³(104-digit number)

10249734207068622648…02062172820278835201

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