Block #275,431

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 5:04:14 PM · Difficulty 9.9608 · 6,534,470 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5337ab54a0c9566088182400debebb0d01c5e3c37e8ba4dd1dfbc29aa4584e32

View on Chainz ↗

Height

#275,431

Difficulty

9.960756

Transactions

Size

4.15 KB

Version

Bits

09f5f419

Nonce

155,304

Timestamp

11/26/2013, 5:04:14 PM

Confirmations

6,534,470

Mined by

⛏️ P2SHAQmhVit2E4HhjNTMSG1bXdp9g89HPyJpi9

Merkle Root

7ad6c0b85f390f1ffe41998f3dbfa26e79cdae339b03d10de9542b8d58766b69

Transactions (4)

Coinbasef7cb0f85ff70c8…18f9d2fe9afa51

1 in → 1 out10.1200 XPM109 B

AQmhVit2…9HPyJpi9

25290963448cad…aaa7bd51882133

5 in → 1 out94.9900 XPM785 B

AY5Rm8Kg…xny2v2QJ

179b35d50aebd3…4289f814525366

19 in → 2 out3.0198 XPM2.82 KB

AJVe1u1Z…B4r1JrVC AJUMEyao…hxQTYMK9

8b7a9da45e60d3…d3c3bcca976278

2 in → 2 out4.8472 XPM374 B

AP6HDxaK…Q1Go96SR AYFydYzP…niTUbHMP

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.

1.564 × 10⁹⁵(96-digit number)

15644533656863495726…97702451226373090079

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

1.564 × 10⁹⁵(96-digit number)

15644533656863495726…97702451226373090079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.564 × 10⁹⁵(96-digit number)

15644533656863495726…97702451226373090081

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

3.128 × 10⁹⁵(96-digit number)

31289067313726991452…95404902452746180159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.128 × 10⁹⁵(96-digit number)

31289067313726991452…95404902452746180161

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

6.257 × 10⁹⁵(96-digit number)

62578134627453982905…90809804905492360319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.257 × 10⁹⁵(96-digit number)

62578134627453982905…90809804905492360321

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

1.251 × 10⁹⁶(97-digit number)

12515626925490796581…81619609810984720639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.251 × 10⁹⁶(97-digit number)

12515626925490796581…81619609810984720641

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

2.503 × 10⁹⁶(97-digit number)

25031253850981593162…63239219621969441279

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 #275,431

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