Block #150,953

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/5/2013, 9:25:52 AM · Difficulty 9.8589 · 6,654,186 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b2410d6ba9142f1799e7211589ad1e6c6e7298bab51a149858376d47ad99366c

View on Chainz ↗

Height

#150,953

Difficulty

9.858903

Transactions

Size

1.64 KB

Version

Bits

09dbe110

Nonce

212,686

Timestamp

9/5/2013, 9:25:52 AM

Confirmations

6,654,186

Mined by

⛏️ P2SHAbERMcutQDScg9DXkU4LAqx7CDQQKtkzeK

Merkle Root

46728f5cd780c3f94ed4521369b8e9a594bcca5743a0bed08ef426265fb4f7f6

Transactions (2)

Coinbase6b960a69cc50b9…501bb000fc6dd5

1 in → 1 out10.2900 XPM109 B

AbERMcut…QQKtkzeK

5d1555fda2f803…2e821eab5afb70

12 in → 2 out119.6900 XPM1.45 KB

ARs3PPit…jsaDGrQD 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.

6.158 × 10⁹³(94-digit number)

61583241870277432166…10995167175365093419

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

6.158 × 10⁹³(94-digit number)

61583241870277432166…10995167175365093419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.158 × 10⁹³(94-digit number)

61583241870277432166…10995167175365093421

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

1.231 × 10⁹⁴(95-digit number)

12316648374055486433…21990334350730186839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.231 × 10⁹⁴(95-digit number)

12316648374055486433…21990334350730186841

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

2.463 × 10⁹⁴(95-digit number)

24633296748110972866…43980668701460373679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.463 × 10⁹⁴(95-digit number)

24633296748110972866…43980668701460373681

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

4.926 × 10⁹⁴(95-digit number)

49266593496221945733…87961337402920747359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.926 × 10⁹⁴(95-digit number)

49266593496221945733…87961337402920747361

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

9.853 × 10⁹⁴(95-digit number)

98533186992443891466…75922674805841494719

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