Block #274,070

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 3:23:43 AM · Difficulty 9.9562 · 6,517,264 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

121398722ed1f6675540d8d2f41ca6ed3a9f2cabc5bf5a86eac22438fc96fade

View on Chainz ↗

Height

#274,070

Difficulty

9.956250

Transactions

Size

66.28 KB

Version

Bits

09f4ccca

Nonce

1,233

Timestamp

11/26/2013, 3:23:43 AM

Confirmations

6,517,264

Merkle Root

662f460d43aed62a76485e0b24f7fd12106b43d2668a87f197d62f6b972ea9fe

Transactions (3)

Coinbase832161ec2e049d…fd01e7e57e04c4

1 in → 2 out10.7500 XPM142 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

f11ded90916017…e5ba12219b4052

5 in → 2 out287.1142 XPM819 B

AW2CXpZm…76nGhG8u AenCYDdj…8yiqcera

0dc323ee79c524…38be1e8de5e377

451 in → 2 out178.6520 XPM65.25 KB

AahjNwBn…qQfzitwc AcGMMPby…s4Jj7MCS

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.

1.005 × 10¹⁰⁴(105-digit number)

10050061943268494190…63604323390483436159

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

1.005 × 10¹⁰⁴(105-digit number)

10050061943268494190…63604323390483436159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.005 × 10¹⁰⁴(105-digit number)

10050061943268494190…63604323390483436161

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

2.010 × 10¹⁰⁴(105-digit number)

20100123886536988381…27208646780966872319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.010 × 10¹⁰⁴(105-digit number)

20100123886536988381…27208646780966872321

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

4.020 × 10¹⁰⁴(105-digit number)

40200247773073976763…54417293561933744639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.020 × 10¹⁰⁴(105-digit number)

40200247773073976763…54417293561933744641

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

8.040 × 10¹⁰⁴(105-digit number)

80400495546147953527…08834587123867489279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.040 × 10¹⁰⁴(105-digit number)

80400495546147953527…08834587123867489281

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

1.608 × 10¹⁰⁵(106-digit number)

16080099109229590705…17669174247734978559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.608 × 10¹⁰⁵(106-digit number)

16080099109229590705…17669174247734978561

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