Block #455,505

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/22/2014, 2:30:13 PM · Difficulty 10.4112 · 6,355,451 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fd543290e6f37ed39bcf8a635d6ab44012f8e0a1ab2ed6e5da9ee2f6b28cf0b0

View on Chainz ↗

Height

#455,505

Difficulty

10.411234

Transactions

Size

1.08 KB

Version

Bits

0a6946a7

Nonce

3,900

Timestamp

3/22/2014, 2:30:13 PM

Confirmations

6,355,451

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

d29ce4e059ff6ec9c2ad004666dc4ccf18e8700eec873abd9167f25c79d8e3f6

Transactions (5)

Coinbase47ca602cd5a483…a594101e91215a

1 in → 1 out9.2500 XPM116 B

AbwWkWZt…kawDhufa

40a1a4f5d45eb8…27c2f71c05cd49

1 in → 2 out187.4419 XPM225 B

AGfPLwmR…zdWV2tCo AVvRMgBj…Jb5GpDTb

d859776d0255cc…fe66a2965a3e2b

1 in → 2 out3.1799 XPM226 B

AVeCEYGh…S8p5PmZC AeEpqMsk…khoKB2a5

563e32cbe6fd49…806b0645f3ecdf

1 in → 2 out1.0397 XPM225 B

AQg1Fgxm…AyRak15T Ac3aiRgM…z1NXTBEd

31095246199883…add3451a3e79c9

1 in → 2 out2.9968 XPM226 B

AMNCsDeK…6ZBsricT AWrBkyXj…1DRLqgKK

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.

8.431 × 10¹⁰⁰(101-digit number)

84310699217661895514…51884526099790781439

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

8.431 × 10¹⁰⁰(101-digit number)

84310699217661895514…51884526099790781439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.431 × 10¹⁰⁰(101-digit number)

84310699217661895514…51884526099790781441

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

1.686 × 10¹⁰¹(102-digit number)

16862139843532379102…03769052199581562879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.686 × 10¹⁰¹(102-digit number)

16862139843532379102…03769052199581562881

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

3.372 × 10¹⁰¹(102-digit number)

33724279687064758205…07538104399163125759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.372 × 10¹⁰¹(102-digit number)

33724279687064758205…07538104399163125761

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

6.744 × 10¹⁰¹(102-digit number)

67448559374129516411…15076208798326251519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.744 × 10¹⁰¹(102-digit number)

67448559374129516411…15076208798326251521

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

1.348 × 10¹⁰²(103-digit number)

13489711874825903282…30152417596652503039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.348 × 10¹⁰²(103-digit number)

13489711874825903282…30152417596652503041

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 #455,505

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