Block #134,961

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/26/2013, 8:46:19 AM · Difficulty 9.8072 · 6,673,775 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

31aa80a30b68f73168c6b35f189fafa90b9769aeea65590887f43d56e9e08b36

View on Chainz ↗

Height

#134,961

Difficulty

9.807208

Transactions

Size

694 B

Version

Bits

09cea52b

Nonce

91,349

Timestamp

8/26/2013, 8:46:19 AM

Confirmations

6,673,775

Mined by

⛏️ P2SHAL4on7MoehvKsN2qMpn6JMVQDzcZpCa12j

Merkle Root

7eeb4679e58c70916cae989e0852d5228d81e56d7ac02bdfce1fc1d6109da3cd

Transactions (2)

Coinbaseb224de78780a3b…923edf99bea40b

1 in → 1 out10.3900 XPM109 B

AL4on7Mo…cZpCa12j

9a0547fc4c9707…1b3725a0ef01d9

4 in → 1 out41.7400 XPM497 B

AWnaiAPB…NVoViQC6

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.

8.086 × 10⁸⁸(89-digit number)

80865859709383957822…53033911069978391799

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

8.086 × 10⁸⁸(89-digit number)

80865859709383957822…53033911069978391799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.086 × 10⁸⁸(89-digit number)

80865859709383957822…53033911069978391801

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

1.617 × 10⁸⁹(90-digit number)

16173171941876791564…06067822139956783599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.617 × 10⁸⁹(90-digit number)

16173171941876791564…06067822139956783601

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

3.234 × 10⁸⁹(90-digit number)

32346343883753583129…12135644279913567199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.234 × 10⁸⁹(90-digit number)

32346343883753583129…12135644279913567201

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

6.469 × 10⁸⁹(90-digit number)

64692687767507166258…24271288559827134399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.469 × 10⁸⁹(90-digit number)

64692687767507166258…24271288559827134401

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

1.293 × 10⁹⁰(91-digit number)

12938537553501433251…48542577119654268799

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 #134,961

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