Block #309,208

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/13/2013, 11:57:25 AM · Difficulty 9.9948 · 6,501,395 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

29cf42392cacb9a53316392aa345cf0586b1cd0d684afe5c5c8b435d52463105

View on Chainz ↗

Height

#309,208

Difficulty

9.994753

Transactions

Size

1.11 KB

Version

Bits

09fea820

Nonce

28,316

Timestamp

12/13/2013, 11:57:25 AM

Confirmations

6,501,395

Mined by

⛏️ aR%AZ2pPuKgN7GXPJPBLxtm9bkWcE95SN2Yr7

Merkle Root

552cf4896511cbfbcc56b88e426bab817dca8717c00daef0a3407b890eb1d065

Transactions (1)

Coinbase552cf4896511cb…407b890eb1d065

1 in → 29 out9.9800 XPM1.02 KB

AZ2pPuKg…95SN2Yr7 Aac9Hjdg…P4ktypc3 AYcLTeXR…bscgPops AcM3ext6…Hwtj9Qp3 AN5MXfjX…u4P4vFee

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.

1.076 × 10⁹²(93-digit number)

10766683762246208019…34546099821666287099

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

1.076 × 10⁹²(93-digit number)

10766683762246208019…34546099821666287099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.076 × 10⁹²(93-digit number)

10766683762246208019…34546099821666287101

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

2.153 × 10⁹²(93-digit number)

21533367524492416038…69092199643332574199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.153 × 10⁹²(93-digit number)

21533367524492416038…69092199643332574201

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

4.306 × 10⁹²(93-digit number)

43066735048984832076…38184399286665148399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.306 × 10⁹²(93-digit number)

43066735048984832076…38184399286665148401

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

8.613 × 10⁹²(93-digit number)

86133470097969664153…76368798573330296799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.613 × 10⁹²(93-digit number)

86133470097969664153…76368798573330296801

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

1.722 × 10⁹³(94-digit number)

17226694019593932830…52737597146660593599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.722 × 10⁹³(94-digit number)

17226694019593932830…52737597146660593601

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 #309,208

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