Block #274,746

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 10:10:28 AM · Difficulty 9.9585 · 6,523,066 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

70a8b55161fb434eb921f772a83c4ab783d5f334d76003dee4b997519d143bc7

View on Chainz ↗

Height

#274,746

Difficulty

9.958549

Transactions

Size

3.92 KB

Version

Bits

09f56374

Nonce

3,319

Timestamp

11/26/2013, 10:10:28 AM

Confirmations

6,523,066

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

e69b30ae0a1fcb77b894087d7a091555554c112575f17a6c15291623d5f87799

Transactions (2)

Coinbased3a433918eb1b8…6ee56ea4a5d568

1 in → 2 out10.1100 XPM142 B

AKcbk49N…GJbKa7j1 AKNbfPoc…jfkpwAyL

75cf7c32fc175d…b88d6492b818ef

25 in → 2 out693.0100 XPM3.69 KB

AK9G4b1G…9rqGGqPf Ac8t1vd5…WkKm3tSr

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.

6.118 × 10¹⁰³(104-digit number)

61189464935120003226…07154098326049704559

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

6.118 × 10¹⁰³(104-digit number)

61189464935120003226…07154098326049704559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.118 × 10¹⁰³(104-digit number)

61189464935120003226…07154098326049704561

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

1.223 × 10¹⁰⁴(105-digit number)

12237892987024000645…14308196652099409119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.223 × 10¹⁰⁴(105-digit number)

12237892987024000645…14308196652099409121

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

2.447 × 10¹⁰⁴(105-digit number)

24475785974048001290…28616393304198818239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.447 × 10¹⁰⁴(105-digit number)

24475785974048001290…28616393304198818241

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

4.895 × 10¹⁰⁴(105-digit number)

48951571948096002581…57232786608397636479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.895 × 10¹⁰⁴(105-digit number)

48951571948096002581…57232786608397636481

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

9.790 × 10¹⁰⁴(105-digit number)

97903143896192005162…14465573216795272959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.790 × 10¹⁰⁴(105-digit number)

97903143896192005162…14465573216795272961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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