Block #135,116

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/26/2013, 10:46:23 AM · Difficulty 9.8085 · 6,667,577 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8410eb882ac375d16d4935e7b2fd7f27d95a4e90878b5e1f2f231643c183ef5a

View on Chainz ↗

Height

#135,116

Difficulty

9.808489

Transactions

Size

1.00 KB

Version

Bits

09cef922

Nonce

52,370

Timestamp

8/26/2013, 10:46:23 AM

Confirmations

6,667,577

Mined by

⛏️ P2SHAcprKFHC4Fvm4QCAFyZqCh4ovAD4cVWMLN

Merkle Root

bb2089faf11ac604e1f5707595e968cd1a8d665dcb4a36d903036992b93abe15

Transactions (4)

Coinbase78c01a9c2b6369…6b7161daeb5847

1 in → 1 out10.4100 XPM109 B

AcprKFHC…D4cVWMLN

f8b4367061fa59…df13e08d30ea35

2 in → 2 out20.8500 XPM375 B

AaamjEDB…UqchbkWj ALbKHFq9…8jP4jk1Q

59eca8927bf7c9…62bb3dc2ba5bc4

1 in → 2 out3.2831 XPM225 B

AZhEpBAV…N9P47GNd ALz3uSwR…DHKjj4EL

9d361cf5fb2c41…0b42d99d8db6a4

1 in → 2 out2.1319 XPM226 B

ALhRSj2t…ho5CrkLo AaTLFhkh…9mU4dVMh

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.

7.020 × 10⁹⁴(95-digit number)

70201369186501155408…25451296594913325609

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

7.020 × 10⁹⁴(95-digit number)

70201369186501155408…25451296594913325609

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.020 × 10⁹⁴(95-digit number)

70201369186501155408…25451296594913325611

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

1.404 × 10⁹⁵(96-digit number)

14040273837300231081…50902593189826651219

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.404 × 10⁹⁵(96-digit number)

14040273837300231081…50902593189826651221

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

2.808 × 10⁹⁵(96-digit number)

28080547674600462163…01805186379653302439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.808 × 10⁹⁵(96-digit number)

28080547674600462163…01805186379653302441

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

5.616 × 10⁹⁵(96-digit number)

56161095349200924326…03610372759306604879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.616 × 10⁹⁵(96-digit number)

56161095349200924326…03610372759306604881

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

1.123 × 10⁹⁶(97-digit number)

11232219069840184865…07220745518613209759

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