Block #496,872

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2014, 7:35:28 AM · Difficulty 10.7601 · 6,312,977 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f924e2905abb5713a4bf878177b55b1633cc088901c67f38220ae752d4b48547

View on Chainz ↗

Height

#496,872

Difficulty

10.760139

Transactions

Size

1.25 KB

Version

Bits

0ac2987c

Nonce

82,494,399

Timestamp

4/17/2014, 7:35:28 AM

Confirmations

6,312,977

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

698562610d47524c6ea01013a9cfa51d3a3195346f06e6cac482e27abbeec89f

Transactions (4)

Coinbase82af1126f7459a…7d232f4c778ff5

1 in → 1 out8.6500 XPM116 B

AbwWkWZt…kawDhufa

1cb868ecd3a225…75b065ada871fb

3 in → 8 out26.1300 XPM622 B

AJ1Rg4tk…5YkqEmTH AW9UAps1…PoAQ39bN AKy4P26p…bxEZW13i AXbbkuVv…UixHY7hn AeKNrjNj…1NEq95Ta

8e07e9a0de4a88…04cccdcd2c962d

1 in → 2 out8.7000 XPM226 B

AYFip19m…wnrKi5Ai AN3i2ZyN…MkpoEvc1

71788c7ebda040…649da12c9240f5

1 in → 2 out8.7000 XPM226 B

ARJSQLHK…aRN2qK1s AULkviz4…6ZwMzqc9

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.

8.301 × 10⁹⁹(100-digit number)

83014442914782720373…20385729331797135359

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

8.301 × 10⁹⁹(100-digit number)

83014442914782720373…20385729331797135359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.301 × 10⁹⁹(100-digit number)

83014442914782720373…20385729331797135361

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

1.660 × 10¹⁰⁰(101-digit number)

16602888582956544074…40771458663594270719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.660 × 10¹⁰⁰(101-digit number)

16602888582956544074…40771458663594270721

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

3.320 × 10¹⁰⁰(101-digit number)

33205777165913088149…81542917327188541439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.320 × 10¹⁰⁰(101-digit number)

33205777165913088149…81542917327188541441

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

6.641 × 10¹⁰⁰(101-digit number)

66411554331826176299…63085834654377082879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.641 × 10¹⁰⁰(101-digit number)

66411554331826176299…63085834654377082881

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

1.328 × 10¹⁰¹(102-digit number)

13282310866365235259…26171669308754165759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.328 × 10¹⁰¹(102-digit number)

13282310866365235259…26171669308754165761

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 #496,872

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