Block #791,081

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/31/2014, 7:04:24 PM · Difficulty 10.9733 · 6,013,959 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a4602ecbd546ba15ad240e5c0c9f85d49ce0b5e317bc643083c215762c9fbc47

View on Chainz ↗

Height

#791,081

Difficulty

10.973280

Transactions

Size

956 B

Version

Bits

0af928e0

Nonce

448,746,299

Timestamp

10/31/2014, 7:04:24 PM

Confirmations

6,013,959

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

984eaed55b562ac0ce0ad6f8f21ca45aee1b7eb734e133bc5b1a70611115c6c7

Transactions (3)

Coinbase418ad4d766fced…a2f7ef5fe315af

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

863eb87d743626…e2a8a755a75a53

3 in → 2 out179.5500 XPM523 B

AQUC7Hue…LL2XMoNY AJa7diLx…UWUZH3qC

1a48e5188db353…255f7274ed0fb5

1 in → 2 out1.4278 XPM227 B

AQTBpkfG…cmM2cJGR Ae7YXEyn…hnSYZsCr

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.

1.180 × 10⁹⁵(96-digit number)

11807002823547958523…09683836730877511759

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

1.180 × 10⁹⁵(96-digit number)

11807002823547958523…09683836730877511759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.180 × 10⁹⁵(96-digit number)

11807002823547958523…09683836730877511761

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

2.361 × 10⁹⁵(96-digit number)

23614005647095917047…19367673461755023519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.361 × 10⁹⁵(96-digit number)

23614005647095917047…19367673461755023521

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

4.722 × 10⁹⁵(96-digit number)

47228011294191834094…38735346923510047039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.722 × 10⁹⁵(96-digit number)

47228011294191834094…38735346923510047041

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

9.445 × 10⁹⁵(96-digit number)

94456022588383668188…77470693847020094079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.445 × 10⁹⁵(96-digit number)

94456022588383668188…77470693847020094081

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

1.889 × 10⁹⁶(97-digit number)

18891204517676733637…54941387694040188159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.889 × 10⁹⁶(97-digit number)

18891204517676733637…54941387694040188161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.778 × 10⁹⁶(97-digit number)

37782409035353467275…09882775388080376319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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