Block #274,180

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 4:35:10 AM · Difficulty 9.9566 · 6,534,736 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f650f4cf556e5942a6bd9df8fc0bdc018955148de9eba5bbbb1c8a25606296a2

View on Chainz ↗

Height

#274,180

Difficulty

9.956596

Transactions

Size

2.07 KB

Version

Bits

09f4e382

Nonce

3,292

Timestamp

11/26/2013, 4:35:10 AM

Confirmations

6,534,736

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

f939f9a8551e641f71b879e5cab938b22b353cb64c65a60b1f0dae80b6fd32f4

Transactions (3)

Coinbasecb042322ae265a…da587bb5628b74

1 in → 2 out10.1000 XPM141 B

AKcbk49N…GJbKa7j1 AHsw4d6U…EnM8UXNZ

977c85fd9ee8a1…42b3cfaaacd5fa

9 in → 13 out86.1726 XPM1.47 KB

ANWcCA1W…FYxSHbqJ AbrxnfNC…nEpWGHhc AYbYVJcZ…x7tzQXTv AMsrZhpd…pYrYdaoi AWtxvHFo…8goMQkVK

34c9adabee560f…a790d410ca0621

2 in → 2 out9.6930 XPM375 B

AQgHQMax…E4MyNtKS AeZCKRPy…9yRziABL

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.

3.881 × 10¹⁰³(104-digit number)

38812224899527074371…41673921501418015039

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

3.881 × 10¹⁰³(104-digit number)

38812224899527074371…41673921501418015039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.881 × 10¹⁰³(104-digit number)

38812224899527074371…41673921501418015041

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

7.762 × 10¹⁰³(104-digit number)

77624449799054148743…83347843002836030079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.762 × 10¹⁰³(104-digit number)

77624449799054148743…83347843002836030081

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

1.552 × 10¹⁰⁴(105-digit number)

15524889959810829748…66695686005672060159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.552 × 10¹⁰⁴(105-digit number)

15524889959810829748…66695686005672060161

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

3.104 × 10¹⁰⁴(105-digit number)

31049779919621659497…33391372011344120319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.104 × 10¹⁰⁴(105-digit number)

31049779919621659497…33391372011344120321

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

6.209 × 10¹⁰⁴(105-digit number)

62099559839243318994…66782744022688240639

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 #274,180

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