Block #302,943

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2013, 2:37:17 AM · Difficulty 9.9929 · 6,492,255 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

29440671fd1df1aa7612fcf6fa06af277c6a79669bd9e642d582924334c3289c

View on Chainz ↗

Height

#302,943

Difficulty

9.992865

Transactions

Size

2.48 KB

Version

Bits

09fe2c60

Nonce

150,564

Timestamp

12/10/2013, 2:37:17 AM

Confirmations

6,492,255

Mined by

⛏️ _aR~~Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

82c211cec9b2cfc7b160202fca9022d772aa9465aeb884627642bda4c5a1d9a6

Transactions (4)

Coinbase999f85cb560608…e55bc40210b0cd

1 in → 26 out10.0000 XPM947 B

Ad9pSzHt…cpJ3y2zz AWZd1qVJ…9pj9yfPa AYcLTeXR…bscgPops AQf7sjuh…sNY5fXpu ARcqMJhp…RVLToQ6S

e6a035b4f9b431…3322a9e137b58a

1 in → 2 out72.4756 XPM227 B

ALJcCDn9…HDJyavtb AKqgFT6k…ztb3k2nk

86017b68381a67…083474e82d3a1b

5 in → 14 out50.2400 XPM1.03 KB

AY3khjqG…rSbvt2VJ AcEmwC3r…QwphbcFh ATz1Sryu…PWZHWKYx AVLbPnVT…MXTBm469 AVRSjnEd…SARf4wT4

238b33afa73af4…f960aaf2a2dbaf

1 in → 2 out6.6488 XPM226 B

ANETVGAM…czZK7qqh ALkSEop5…pbUrFQKu

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.

2.374 × 10⁹³(94-digit number)

23740300629801689216…73245743409125387499

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

2.374 × 10⁹³(94-digit number)

23740300629801689216…73245743409125387499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.374 × 10⁹³(94-digit number)

23740300629801689216…73245743409125387501

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

4.748 × 10⁹³(94-digit number)

47480601259603378432…46491486818250774999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.748 × 10⁹³(94-digit number)

47480601259603378432…46491486818250775001

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

9.496 × 10⁹³(94-digit number)

94961202519206756865…92982973636501549999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.496 × 10⁹³(94-digit number)

94961202519206756865…92982973636501550001

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

1.899 × 10⁹⁴(95-digit number)

18992240503841351373…85965947273003099999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.899 × 10⁹⁴(95-digit number)

18992240503841351373…85965947273003100001

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

3.798 × 10⁹⁴(95-digit number)

37984481007682702746…71931894546006199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.798 × 10⁹⁴(95-digit number)

37984481007682702746…71931894546006200001

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