Block #457,778

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/24/2014, 3:34:50 AM · Difficulty 10.4196 · 6,357,171 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b4f11991d49478269c08f6597a7394a4399ccf2285e6764f232e9ba5589a3536

View on Chainz ↗

Height

#457,778

Difficulty

10.419645

Transactions

Size

576 B

Version

Bits

0a6b6dd9

Nonce

118,644

Timestamp

3/24/2014, 3:34:50 AM

Confirmations

6,357,171

Mined by

⛏️ P2SHANskcCBtNAaocvfJZqea17mK899PtdGxeP

Merkle Root

688538cae208a262344e7cda340d2de6b5c1cf6db147f3fbb72cf799efe94526

Transactions (2)

Coinbase1283a29e3fff5a…099b6b29f44aa3

1 in → 1 out9.2100 XPM109 B

ANskcCBt…9PtdGxeP

2b07905f2b9709…68c75c3df0c84b

2 in → 2 out99.8052 XPM374 B

AZ4wTtHZ…v9jxgrXC AaFQdbpN…PiGvSNDu

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.

1.037 × 10¹⁰²(103-digit number)

10370289508258654114…54598459065530058239

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

1.037 × 10¹⁰²(103-digit number)

10370289508258654114…54598459065530058239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.037 × 10¹⁰²(103-digit number)

10370289508258654114…54598459065530058241

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

2.074 × 10¹⁰²(103-digit number)

20740579016517308228…09196918131060116479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.074 × 10¹⁰²(103-digit number)

20740579016517308228…09196918131060116481

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

4.148 × 10¹⁰²(103-digit number)

41481158033034616456…18393836262120232959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.148 × 10¹⁰²(103-digit number)

41481158033034616456…18393836262120232961

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

8.296 × 10¹⁰²(103-digit number)

82962316066069232913…36787672524240465919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.296 × 10¹⁰²(103-digit number)

82962316066069232913…36787672524240465921

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

1.659 × 10¹⁰³(104-digit number)

16592463213213846582…73575345048480931839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.659 × 10¹⁰³(104-digit number)

16592463213213846582…73575345048480931841

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 #457,778

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