Block #82,629

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/25/2013, 1:26:04 PM · Difficulty 9.2763 · 6,708,365 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fea819a886fb0a1dd5713e4e24267bebe8496f74f6a6404f816ce832e5821db8

View on Chainz ↗

Height

#82,629

Difficulty

9.276316

Transactions

Size

577 B

Version

Bits

0946bcad

Nonce

528

Timestamp

7/25/2013, 1:26:04 PM

Confirmations

6,708,365

Merkle Root

2588a84d4c0d1cb5aba928feb80faf08089309f20ca368d6b6863d85c2b1afbd

Transactions (2)

Coinbase82d3654cd1f84a…be33a04254db1e

1 in → 1 out11.6100 XPM110 B

ARBozoCu…atRzp6w5

502c2dcd84116c…05e4a35f1c8687

2 in → 2 out531.9900 XPM375 B

AcU3G17t…7wPGLC6Z AHe2ZDcW…f65kYL5b

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.

3.714 × 10¹⁰⁰(101-digit number)

37146612586970155672…18370883500262239799

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

3.714 × 10¹⁰⁰(101-digit number)

37146612586970155672…18370883500262239799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.714 × 10¹⁰⁰(101-digit number)

37146612586970155672…18370883500262239801

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

7.429 × 10¹⁰⁰(101-digit number)

74293225173940311345…36741767000524479599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.429 × 10¹⁰⁰(101-digit number)

74293225173940311345…36741767000524479601

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

1.485 × 10¹⁰¹(102-digit number)

14858645034788062269…73483534001048959199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.485 × 10¹⁰¹(102-digit number)

14858645034788062269…73483534001048959201

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

2.971 × 10¹⁰¹(102-digit number)

29717290069576124538…46967068002097918399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.971 × 10¹⁰¹(102-digit number)

29717290069576124538…46967068002097918401

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

5.943 × 10¹⁰¹(102-digit number)

59434580139152249076…93934136004195836799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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