Block #501,297

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/19/2014, 5:00:55 PM · Difficulty 10.8031 · 6,307,768 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

94a63c7196262c4d49635afc9f97e4d3fc4054c0d4dea0898513a9bb55b7f2cf

View on Chainz ↗

Height

#501,297

Difficulty

10.803120

Transactions

Size

1.48 KB

Version

Bits

0acd993e

Nonce

340,652,314

Timestamp

4/19/2014, 5:00:55 PM

Confirmations

6,307,768

Mined by

⛏️ 1aSRBAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d2db1c15e3923b70b0d2dadef8d1292704cd6819636b41dfef2becfee6e4f9c6

Transactions (4)

Coinbasef2f2f231d333bd…8fc636ccf8a389

1 in → 20 out8.5500 XPM743 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j AScAzqGc…BZ6tV1vJ

6cfc3f5e8213b4…93c2ea376e6665

1 in → 2 out1184.0800 XPM226 B

AKhJT8Hh…vAmDJ8hK AaHVtG7g…tLxzmTZY

db8bdfff7d73ce…05982dd507c287

1 in → 2 out8.0682 XPM227 B

AKgNP6et…2qQSHMCh AczJNnfo…5jh4mwMK

390c0bbf28af85…ad03e7413701b4

1 in → 2 out7.5772 XPM226 B

AcvcqFVj…uZHXEWhk AM23VEk3…q622MtoH

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.

1.610 × 10¹⁰⁰(101-digit number)

16107681690267548259…49393545294959554559

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

1.610 × 10¹⁰⁰(101-digit number)

16107681690267548259…49393545294959554559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.610 × 10¹⁰⁰(101-digit number)

16107681690267548259…49393545294959554561

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

3.221 × 10¹⁰⁰(101-digit number)

32215363380535096519…98787090589919109119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.221 × 10¹⁰⁰(101-digit number)

32215363380535096519…98787090589919109121

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

6.443 × 10¹⁰⁰(101-digit number)

64430726761070193039…97574181179838218239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.443 × 10¹⁰⁰(101-digit number)

64430726761070193039…97574181179838218241

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

1.288 × 10¹⁰¹(102-digit number)

12886145352214038607…95148362359676436479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.288 × 10¹⁰¹(102-digit number)

12886145352214038607…95148362359676436481

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

2.577 × 10¹⁰¹(102-digit number)

25772290704428077215…90296724719352872959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.577 × 10¹⁰¹(102-digit number)

25772290704428077215…90296724719352872961

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

5.154 × 10¹⁰¹(102-digit number)

51544581408856154431…80593449438705745919

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 #501,297

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