Block #86,299

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 1:07:39 AM · Difficulty 9.2891 · 6,703,540 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e0bafb5e6d5e335ad36ee3ea5d87599d3626dafb64ec0707aed3a1f661948cf7

View on Chainz ↗

Height

#86,299

Difficulty

9.289059

Transactions

Size

206 B

Version

Bits

0949ffc1

Nonce

30,423

Timestamp

7/28/2013, 1:07:39 AM

Confirmations

6,703,540

Merkle Root

20b2edf528040c1ffba14f0adfe766703748801a31f9866004e9a0e0c3f34d33

Transactions (1)

Coinbase20b2edf528040c…e9a0e0c3f34d33

1 in → 1 out11.5700 XPM109 B

AcBadmkp…GmhL921o

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.

7.312 × 10¹¹⁰(111-digit number)

73127032844872988529…36460666072460763999

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

7.312 × 10¹¹⁰(111-digit number)

73127032844872988529…36460666072460763999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.312 × 10¹¹⁰(111-digit number)

73127032844872988529…36460666072460764001

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

1.462 × 10¹¹¹(112-digit number)

14625406568974597705…72921332144921527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.462 × 10¹¹¹(112-digit number)

14625406568974597705…72921332144921528001

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

2.925 × 10¹¹¹(112-digit number)

29250813137949195411…45842664289843055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.925 × 10¹¹¹(112-digit number)

29250813137949195411…45842664289843056001

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

5.850 × 10¹¹¹(112-digit number)

58501626275898390823…91685328579686111999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.850 × 10¹¹¹(112-digit number)

58501626275898390823…91685328579686112001

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

1.170 × 10¹¹²(113-digit number)

11700325255179678164…83370657159372223999

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