Block #283,457

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 5:59:30 PM · Difficulty 9.9812 · 6,526,103 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5b2629297c4ed9585a9bd81645ff4305d516b87043874fb934e78f2a7fd814b

View on Chainz ↗

Height

#283,457

Difficulty

9.981159

Transactions

Size

1.11 KB

Version

Bits

09fb2d36

Nonce

96,328

Timestamp

11/29/2013, 5:59:30 PM

Confirmations

6,526,103

Mined by

⛏️ ASaRAasErbrMRLt6mdduA6H5eenrn5pVctJGSP

Merkle Root

871eb934808259903aaa08bf82cfa77ab7f7a6a86be92fb461630a442f190d5c

Transactions (1)

Coinbase871eb934808259…630a442f190d5c

1 in → 29 out10.0000 XPM1.02 KB

AasErbrM…pVctJGSP AP35e64F…amMs1Qnk AKi14Bc9…xnGApQUN AQyr8Lw3…hs4nt3Pn AZ2pPuKg…95SN2Yr7

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.

6.311 × 10⁹⁵(96-digit number)

63111706534504012660…62238717962258455039

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

6.311 × 10⁹⁵(96-digit number)

63111706534504012660…62238717962258455039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.311 × 10⁹⁵(96-digit number)

63111706534504012660…62238717962258455041

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

1.262 × 10⁹⁶(97-digit number)

12622341306900802532…24477435924516910079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.262 × 10⁹⁶(97-digit number)

12622341306900802532…24477435924516910081

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

2.524 × 10⁹⁶(97-digit number)

25244682613801605064…48954871849033820159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.524 × 10⁹⁶(97-digit number)

25244682613801605064…48954871849033820161

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

5.048 × 10⁹⁶(97-digit number)

50489365227603210128…97909743698067640319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.048 × 10⁹⁶(97-digit number)

50489365227603210128…97909743698067640321

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

1.009 × 10⁹⁷(98-digit number)

10097873045520642025…95819487396135280639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.009 × 10⁹⁷(98-digit number)

10097873045520642025…95819487396135280641

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 #283,457

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