Block #86,896

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 11:39:53 AM · Difficulty 9.2842 · 6,704,604 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0325b8a134dde0497cee4f8de7b17f71bfdfe5a557188387d485f1e1bf353815

View on Chainz ↗

Height

#86,896

Difficulty

9.284170

Transactions

Size

206 B

Version

Bits

0948bf57

Nonce

48,669

Timestamp

7/28/2013, 11:39:53 AM

Confirmations

6,704,604

Merkle Root

d202be4689fb41178aec3da2d7267619908526a89131360ba1b8947ab47dde80

Transactions (1)

Coinbased202be4689fb41…b8947ab47dde80

1 in → 1 out11.5800 XPM109 B

AK1JUKWL…oPR4rN5o

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.

6.095 × 10¹¹²(113-digit number)

60952945993464366586…69976585616215929599

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

6.095 × 10¹¹²(113-digit number)

60952945993464366586…69976585616215929599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.095 × 10¹¹²(113-digit number)

60952945993464366586…69976585616215929601

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

1.219 × 10¹¹³(114-digit number)

12190589198692873317…39953171232431859199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.219 × 10¹¹³(114-digit number)

12190589198692873317…39953171232431859201

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

2.438 × 10¹¹³(114-digit number)

24381178397385746634…79906342464863718399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.438 × 10¹¹³(114-digit number)

24381178397385746634…79906342464863718401

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

4.876 × 10¹¹³(114-digit number)

48762356794771493268…59812684929727436799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.876 × 10¹¹³(114-digit number)

48762356794771493268…59812684929727436801

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

9.752 × 10¹¹³(114-digit number)

97524713589542986537…19625369859454873599

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