Block #306,618

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 3:45:37 AM · Difficulty 9.9939 · 6,497,577 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fde07a3a45ebbd5e265868d7309b7e3b3b9af660663d83075d60899a9ef59ba4

View on Chainz ↗

Height

#306,618

Difficulty

9.993937

Transactions

Size

1.81 KB

Version

Bits

09fe72a7

Nonce

570,207

Timestamp

12/12/2013, 3:45:37 AM

Confirmations

6,497,577

Mined by

⛏️ aR0Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

d6f0b5853e2bd31b6aa4a6b1d8abd0257d6fd322395ac97f38e4284b8ddc80f6

Transactions (4)

Coinbase5535d671becd3e…54327ce210bf4b

1 in → 30 out9.9800 XPM1.06 KB

Ad9pSzHt…cpJ3y2zz AZ2pPuKg…95SN2Yr7 ARXSrG7z…CRW69WR4 AUYNAuZP…XjbXdz8N AcGwkQpJ…nZuUm7Kg

cac64eade67266…877454e19904e0

1 in → 2 out7.9563 XPM227 B

AVdVSwjR…XmTTz5mJ AH5YG9uB…eFEP7MJK

a72680e8d576b7…e594fce74270d8

1 in → 2 out5.9224 XPM226 B

AKmxBBzd…AHmu4uiE AZDfcokA…WhVgHvs4

e89b546fc06702…ad78b5f5b32dbe

1 in → 2 out2.7957 XPM226 B

AR9Zik7j…DzF4KZS7 AJGUbz7a…nDZ1xtce

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.

5.977 × 10⁹⁵(96-digit number)

59772778786696587195…41226332289609859199

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

5.977 × 10⁹⁵(96-digit number)

59772778786696587195…41226332289609859199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.977 × 10⁹⁵(96-digit number)

59772778786696587195…41226332289609859201

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

1.195 × 10⁹⁶(97-digit number)

11954555757339317439…82452664579219718399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.195 × 10⁹⁶(97-digit number)

11954555757339317439…82452664579219718401

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

2.390 × 10⁹⁶(97-digit number)

23909111514678634878…64905329158439436799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.390 × 10⁹⁶(97-digit number)

23909111514678634878…64905329158439436801

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

4.781 × 10⁹⁶(97-digit number)

47818223029357269756…29810658316878873599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.781 × 10⁹⁶(97-digit number)

47818223029357269756…29810658316878873601

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

9.563 × 10⁹⁶(97-digit number)

95636446058714539512…59621316633757747199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.563 × 10⁹⁶(97-digit number)

95636446058714539512…59621316633757747201

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