Block #141,835

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/30/2013, 2:14:29 PM · Difficulty 9.8352 · 6,685,063 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6fad4bb7975338d4a98429ae025257c5c488409b5b401f8bdd791c5d0f644ffc

View on Chainz ↗

Height

#141,835

Difficulty

9.835239

Transactions

Size

1.93 KB

Version

Bits

09d5d23d

Nonce

148,405

Timestamp

8/30/2013, 2:14:29 PM

Confirmations

6,685,063

Mined by

⛏️ P2SHAKTJaBYqzxfxK24bLiUkYxgAvcFdBSY1j1

Merkle Root

617b01c7f09bf2d6d7a231d9e5cd4be0f7866649365ad607447ba32577cb0533

Transactions (2)

Coinbasebee2506b3c6f5e…ae931d113a2dd3

1 in → 1 out10.3400 XPM109 B

AKTJaBYq…FdBSY1j1

5c3d2bd9f00731…6c445b33953ce4

14 in → 2 out117.1700 XPM1.74 KB

ATmrN1KJ…FSmbgUaw AGZvBxxa…shhkwtTn

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.

6.381 × 10⁹⁶(97-digit number)

63815876205574444629…36603622394379449279

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

6.381 × 10⁹⁶(97-digit number)

63815876205574444629…36603622394379449279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.381 × 10⁹⁶(97-digit number)

63815876205574444629…36603622394379449281

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

1.276 × 10⁹⁷(98-digit number)

12763175241114888925…73207244788758898559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.276 × 10⁹⁷(98-digit number)

12763175241114888925…73207244788758898561

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

2.552 × 10⁹⁷(98-digit number)

25526350482229777851…46414489577517797119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.552 × 10⁹⁷(98-digit number)

25526350482229777851…46414489577517797121

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

5.105 × 10⁹⁷(98-digit number)

51052700964459555703…92828979155035594239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.105 × 10⁹⁷(98-digit number)

51052700964459555703…92828979155035594241

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

1.021 × 10⁹⁸(99-digit number)

10210540192891911140…85657958310071188479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #141,835

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