Block #274,327

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 6:09:21 AM · Difficulty 9.9571 · 6,521,196 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e59e3376322e478bf067fba8a26d7a0633c2a67e1b389a118d363febaab8e0f3

View on Chainz ↗

Height

#274,327

Difficulty

9.957050

Transactions

Size

6.75 KB

Version

Bits

09f5013b

Nonce

14,284

Timestamp

11/26/2013, 6:09:21 AM

Confirmations

6,521,196

Mined by

⛏️ jI17183AKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

a6041dfe907f2cc713f4cd38aeb92185df007a3e3a0e787fb6815226a50b6dbd

Transactions (5)

Coinbase6c31a61294007b…6ac590a2e481b4

1 in → 2 out10.1600 XPM141 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

50970eb9d7d0b6…9d3ce513b70aed

21 in → 2 out1000.0100 XPM3.11 KB

AWW1XBfZ…dERCKgXf AYxYExjk…HppPT8uh

eb318c0f9dcac3…e241d50db54327

5 in → 2 out183.2429 XPM816 B

AHbJ1inK…3TE2wvHX AMS5uKPZ…RL5NyghK

5440485edf5135…9041ee0e384b66

1 in → 2 out9.8900 XPM226 B

Ae2yQWtu…XoAx1DMd AeEFDbAk…Qf2gWWpR

8d68d98947b35d…d4f6c655a5938c

16 in → 2 out2.5287 XPM2.39 KB

AU46vdxN…42HoV8BR Aa7PZbgv…kDhN7qtc

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.

1.556 × 10¹⁰⁵(106-digit number)

15560223383419913578…81275838962328063999

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

1.556 × 10¹⁰⁵(106-digit number)

15560223383419913578…81275838962328063999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.556 × 10¹⁰⁵(106-digit number)

15560223383419913578…81275838962328064001

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

3.112 × 10¹⁰⁵(106-digit number)

31120446766839827156…62551677924656127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.112 × 10¹⁰⁵(106-digit number)

31120446766839827156…62551677924656128001

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

6.224 × 10¹⁰⁵(106-digit number)

62240893533679654312…25103355849312255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.224 × 10¹⁰⁵(106-digit number)

62240893533679654312…25103355849312256001

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

1.244 × 10¹⁰⁶(107-digit number)

12448178706735930862…50206711698624511999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.244 × 10¹⁰⁶(107-digit number)

12448178706735930862…50206711698624512001

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

2.489 × 10¹⁰⁶(107-digit number)

24896357413471861724…00413423397249023999

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