Block #268,375

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 2:18:26 AM · Difficulty 9.9572 · 6,537,631 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cc0c3b8b1203ea21f4e37ee03f8f878c6d127e75c70a151d8192666e08609885

View on Chainz ↗

Height

#268,375

Difficulty

9.957195

Transactions

Size

844 B

Version

Bits

09f50ac1

Nonce

133,457

Timestamp

11/22/2013, 2:18:26 AM

Confirmations

6,537,631

Mined by

⛏️ P2SHAXuyFzc6hv8f8KvFYDzCWbFyZarhjjyk2z

Merkle Root

fdcc760b119951fcbb9822430d78dc78ff21f6d9da8bf8ce86d33a56a08810ad

Transactions (4)

Coinbase1b9929f02f6ffb…80931fab7f47b4

1 in → 1 out10.1000 XPM109 B

AXuyFzc6…rhjjyk2z

0c1d02ea593968…cd6b096e127741

1 in → 1 out249.9900 XPM192 B

ATxKBJ9p…cjWdpECw

c0d9ba33c45d81…ebb7b55b377fe9

1 in → 2 out65.3977 XPM227 B

AbZHUQeZ…DP5WAVwo AKribKx4…hHqqMkhD

2dc69fc0a2d7d5…ac291f0cadb489

1 in → 2 out14.4146 XPM225 B

AQaT79Lj…5BwL3kvD ALKnh72F…Kv8ifeVe

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.

5.012 × 10⁹⁶(97-digit number)

50124126533201387040…15381525392406012799

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

5.012 × 10⁹⁶(97-digit number)

50124126533201387040…15381525392406012799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.012 × 10⁹⁶(97-digit number)

50124126533201387040…15381525392406012801

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

1.002 × 10⁹⁷(98-digit number)

10024825306640277408…30763050784812025599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.002 × 10⁹⁷(98-digit number)

10024825306640277408…30763050784812025601

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

2.004 × 10⁹⁷(98-digit number)

20049650613280554816…61526101569624051199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.004 × 10⁹⁷(98-digit number)

20049650613280554816…61526101569624051201

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

4.009 × 10⁹⁷(98-digit number)

40099301226561109632…23052203139248102399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.009 × 10⁹⁷(98-digit number)

40099301226561109632…23052203139248102401

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

8.019 × 10⁹⁷(98-digit number)

80198602453122219265…46104406278496204799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.019 × 10⁹⁷(98-digit number)

80198602453122219265…46104406278496204801

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