Block #310,801

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/14/2013, 6:15:15 AM · Difficulty 9.9953 · 6,505,998 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8b6e99aa049b1fa1efebe6ec96c6134e5ea45edd706d1d2312b88b79557ee9be

View on Chainz ↗

Height

#310,801

Difficulty

9.995291

Transactions

Size

1.11 KB

Version

Bits

09fecb64

Nonce

701,719

Timestamp

12/14/2013, 6:15:15 AM

Confirmations

6,505,998

Mined by

⛏️ aRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

533b67ccbf69865fa01da13d49ad09ce01edd4b91f787974a9803075227ea9c0

Transactions (1)

Coinbase533b67ccbf6986…803075227ea9c0

1 in → 29 out9.9700 XPM1.02 KB

Aac9Hjdg…P4ktypc3 AXmS7tZu…11YypHLP AamykSCW…5Mjzpr7i ARy21REr…6pBWtQJ2 AdCiRYVB…DUhULsTZ

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.

8.250 × 10⁹⁴(95-digit number)

82508752953203864797…70552170884386968899

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

8.250 × 10⁹⁴(95-digit number)

82508752953203864797…70552170884386968899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.250 × 10⁹⁴(95-digit number)

82508752953203864797…70552170884386968901

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

1.650 × 10⁹⁵(96-digit number)

16501750590640772959…41104341768773937799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.650 × 10⁹⁵(96-digit number)

16501750590640772959…41104341768773937801

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

3.300 × 10⁹⁵(96-digit number)

33003501181281545918…82208683537547875599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.300 × 10⁹⁵(96-digit number)

33003501181281545918…82208683537547875601

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

6.600 × 10⁹⁵(96-digit number)

66007002362563091837…64417367075095751199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.600 × 10⁹⁵(96-digit number)

66007002362563091837…64417367075095751201

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

1.320 × 10⁹⁶(97-digit number)

13201400472512618367…28834734150191502399

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

Block #310,801

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