Block #271,571

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 5:20:35 PM · Difficulty 9.9520 · 6,523,492 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6c4648785ee5b401d8e4a673ba11f301e7e2e93cd2c5547943d8c00b8fe10a5c

View on Chainz ↗

Height

#271,571

Difficulty

9.952029

Transactions

Size

2.30 KB

Version

Bits

09f3b829

Nonce

685

Timestamp

11/24/2013, 5:20:35 PM

Confirmations

6,523,492

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

eb415d9295d497181c8b231999e8ceb9f1134ea05905f261f3239363c39fd242

Transactions (4)

Coinbaseea2ea5034c3751…9ec3b8cb2e5595

1 in → 2 out10.1200 XPM141 B

AKcbk49N…GJbKa7j1 Abiw8n3q…ZnZfgvQW

45dbe2d9d45b62…4bc57ca53d28d5

3 in → 2 out790.9524 XPM524 B

ALgNw7bk…YjkTkDiB Af2AePh9…8VUChHFD

09dc19ec9d765b…73d0fdbc4a6a9f

2 in → 2 out15.0103 XPM373 B

AcUfLPXg…XAioY58o AKZWG23d…5GYzFkdA

2bf9ee5718cf1d…62500b5bdc4be2

8 in → 1 out8.5790 XPM1.20 KB

AGYjf7BW…vvCt88LL

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.

5.329 × 10¹⁰²(103-digit number)

53295444557745131069…96148912985410896269

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

5.329 × 10¹⁰²(103-digit number)

53295444557745131069…96148912985410896269

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.329 × 10¹⁰²(103-digit number)

53295444557745131069…96148912985410896271

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

1.065 × 10¹⁰³(104-digit number)

10659088911549026213…92297825970821792539

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.065 × 10¹⁰³(104-digit number)

10659088911549026213…92297825970821792541

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

2.131 × 10¹⁰³(104-digit number)

21318177823098052427…84595651941643585079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.131 × 10¹⁰³(104-digit number)

21318177823098052427…84595651941643585081

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

4.263 × 10¹⁰³(104-digit number)

42636355646196104855…69191303883287170159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.263 × 10¹⁰³(104-digit number)

42636355646196104855…69191303883287170161

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

8.527 × 10¹⁰³(104-digit number)

85272711292392209711…38382607766574340319

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