Block #295,444

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/5/2013, 11:05:43 AM · Difficulty 9.9914 · 6,515,632 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5cf6f11c98561b657f2135c03dbf1d1c3642d904590267be741a6de5b3ad69e0

View on Chainz ↗

Height

#295,444

Difficulty

9.991362

Transactions

Size

1.44 KB

Version

Bits

09fdc9e6

Nonce

43,511

Timestamp

12/5/2013, 11:05:43 AM

Confirmations

6,515,632

Mined by

⛏️ P2SHAT4Pt5N9yZ63S6mUsYyGDjAwEjz8Z5Wfkh

Merkle Root

787fa4af416d456eee8e8411c5af846c95123924caa9d77906290f841bf8c478

Transactions (5)

Coinbase4fe4ff27f91d0c…5de7944366e6a5

1 in → 1 out10.0500 XPM109 B

AT4Pt5N9…z8Z5Wfkh

dc22680b5a18b4…1adf4e65f72848

1 in → 1 out10.6000 XPM192 B

ATEvMK5S…ijh2nyJF

2ce4b088b4d019…54b351bdcdf331

1 in → 2 out2.0674 XPM226 B

AXBfMBUx…fjmEScpL ATWFEDyJ…5zMJEBWo

f10e15f1ff2e35…ccb01bc62731ec

4 in → 2 out13.3389 XPM669 B

AViyKNRU…TxDDUfv4 AYJEKchL…FPuck7k5

2f6db196167ab1…21714cf6e04d45

1 in → 1 out82.6847 XPM191 B

AHJnMUH3…brU85i8L

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.

1.304 × 10⁹⁵(96-digit number)

13044968491791838915…70843178779768204799

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

1.304 × 10⁹⁵(96-digit number)

13044968491791838915…70843178779768204799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.304 × 10⁹⁵(96-digit number)

13044968491791838915…70843178779768204801

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

2.608 × 10⁹⁵(96-digit number)

26089936983583677830…41686357559536409599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.608 × 10⁹⁵(96-digit number)

26089936983583677830…41686357559536409601

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

5.217 × 10⁹⁵(96-digit number)

52179873967167355660…83372715119072819199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.217 × 10⁹⁵(96-digit number)

52179873967167355660…83372715119072819201

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

1.043 × 10⁹⁶(97-digit number)

10435974793433471132…66745430238145638399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.043 × 10⁹⁶(97-digit number)

10435974793433471132…66745430238145638401

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

2.087 × 10⁹⁶(97-digit number)

20871949586866942264…33490860476291276799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.087 × 10⁹⁶(97-digit number)

20871949586866942264…33490860476291276801

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 #295,444

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