Block #306,550

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 2:45:29 AM · Difficulty 9.9939 · 6,507,381 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e05768cc991d653a5e2c94416d62fdeb20da2101bdd3963d6077be0d2c2b77c7

View on Chainz ↗

Height

#306,550

Difficulty

9.993921

Transactions

Size

2.08 KB

Version

Bits

09fe719e

Nonce

67,243

Timestamp

12/12/2013, 2:45:29 AM

Confirmations

6,507,381

Mined by

⛏️ vaR#<Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

1e532dd07972a4f597ab8ec17a8c5596122a583db0af45d5afbe0da878ba85aa

Transactions (2)

Coinbase368432aad1547f…5ffea02c3bdb3c

1 in → 29 out9.9730 XPM1.02 KB

Ad9pSzHt…cpJ3y2zz AZ2pPuKg…95SN2Yr7 AXmS7tZu…11YypHLP Ae6gEbs5…m5Mn8oYw AZemWJAo…6jhDtieG

b333fc679acb41…036adf1d057438

5 in → 9 out24.5075 XPM988 B

AeCbZh4r…u2hpjsZN AeRH4qqg…NSGGodJK Ac6airDC…TBiZw3U2 AQxJ1VVp…i5Wf3MsE AM6M7ug7…EArLB49G

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.

7.122 × 10⁹⁰(91-digit number)

71223560804294334653…85133203189105226999

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

7.122 × 10⁹⁰(91-digit number)

71223560804294334653…85133203189105226999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.122 × 10⁹⁰(91-digit number)

71223560804294334653…85133203189105227001

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

1.424 × 10⁹¹(92-digit number)

14244712160858866930…70266406378210453999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.424 × 10⁹¹(92-digit number)

14244712160858866930…70266406378210454001

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

2.848 × 10⁹¹(92-digit number)

28489424321717733861…40532812756420907999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.848 × 10⁹¹(92-digit number)

28489424321717733861…40532812756420908001

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

5.697 × 10⁹¹(92-digit number)

56978848643435467723…81065625512841815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.697 × 10⁹¹(92-digit number)

56978848643435467723…81065625512841816001

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

1.139 × 10⁹²(93-digit number)

11395769728687093544…62131251025683631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.139 × 10⁹²(93-digit number)

11395769728687093544…62131251025683632001

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 #306,550

Cookie Preferences