Block #783,454

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/26/2014, 5:04:57 AM · Difficulty 10.9751 · 6,026,607 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

edc31d0ab6c7989974db38afb4a695a86f10b018ee7db3ffc49fc341ad0fa84d

View on Chainz ↗

Height

#783,454

Difficulty

10.975084

Transactions

Size

16.98 KB

Version

Bits

0af99f22

Nonce

569,968,116

Timestamp

10/26/2014, 5:04:57 AM

Confirmations

6,026,607

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

bf2502af7d1ee7e0b7cae29901f806e96989a99734a2b8c9f52b698c81290dbc

Transactions (3)

Coinbaseb74cbef7597b85…c0510671b88637

1 in → 1 out8.4700 XPM116 B

ANSXnLY2…Sd25TjkD

41e32697cc41ab…997a899807fdd0

110 in → 2 out500.0100 XPM15.97 KB

AJjnK9uC…VreFquR4 ASW6vVj1…bunWqQgK

dbfa036d35d0a7…f702081d812c67

5 in → 2 out1.0340 XPM820 B

AZFCszA5…YEbKqMZo AWXoUJQ8…oPmr94Rn

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.

1.261 × 10⁹⁶(97-digit number)

12613555465782334208…32252011266568315839

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

1.261 × 10⁹⁶(97-digit number)

12613555465782334208…32252011266568315839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.261 × 10⁹⁶(97-digit number)

12613555465782334208…32252011266568315841

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

2.522 × 10⁹⁶(97-digit number)

25227110931564668416…64504022533136631679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.522 × 10⁹⁶(97-digit number)

25227110931564668416…64504022533136631681

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

5.045 × 10⁹⁶(97-digit number)

50454221863129336833…29008045066273263359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.045 × 10⁹⁶(97-digit number)

50454221863129336833…29008045066273263361

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

1.009 × 10⁹⁷(98-digit number)

10090844372625867366…58016090132546526719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.009 × 10⁹⁷(98-digit number)

10090844372625867366…58016090132546526721

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

2.018 × 10⁹⁷(98-digit number)

20181688745251734733…16032180265093053439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.018 × 10⁹⁷(98-digit number)

20181688745251734733…16032180265093053441

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

4.036 × 10⁹⁷(98-digit number)

40363377490503469466…32064360530186106879

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

Block #783,454

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