Block #280,770

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 7:10:53 PM · Difficulty 9.9754 · 6,529,106 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e4f56728120b93dc67179486875da909f780eb5074cf7e2ba304707583119989

View on Chainz ↗

Height

#280,770

Difficulty

9.975429

Transactions

Size

1.68 KB

Version

Bits

09f9b5bf

Nonce

46,573

Timestamp

11/28/2013, 7:10:53 PM

Confirmations

6,529,106

Mined by

⛏️ HaRHAa9jCRzz2Qkjwux922yw8FoQgjKFpmCDor

Merkle Root

1a53420ec650822ff6fd46e380425f69198c4d117cb8dd9bf11b77f82a99e1ba

Transactions (4)

Coinbase19d6bd54226df5…b6b23abd45879e

1 in → 28 out10.0100 XPM1015 B

Aa9jCRzz…KFpmCDor AUSdJaEr…Y4n4oUzF AZ1U8y3e…CyU6Gm24 AXydriH2…RUoBRJjB AYGGcnmJ…j2K1KoeE

41b547ee197c86…017bfc7979bee4

1 in → 1 out10.0400 XPM159 B

ATV4M1CV…dd9zw8nH

8c663e50a7d7d7…f127ff4c824a5d

1 in → 2 out8.0029 XPM225 B

AH5G1Ccg…D4yYgfhY AV8gFbj9…S6JjsKmU

e241b32f4f550b…b40b9b7c2a22b2

1 in → 2 out8.0002 XPM227 B

AUdrMDs3…Zzet9HNy ALNuV5Jm…EGPqwsoA

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.

1.544 × 10⁹⁶(97-digit number)

15441826902299068367…58200176160712243199

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

1.544 × 10⁹⁶(97-digit number)

15441826902299068367…58200176160712243199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.544 × 10⁹⁶(97-digit number)

15441826902299068367…58200176160712243201

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

3.088 × 10⁹⁶(97-digit number)

30883653804598136734…16400352321424486399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.088 × 10⁹⁶(97-digit number)

30883653804598136734…16400352321424486401

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

6.176 × 10⁹⁶(97-digit number)

61767307609196273469…32800704642848972799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.176 × 10⁹⁶(97-digit number)

61767307609196273469…32800704642848972801

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

1.235 × 10⁹⁷(98-digit number)

12353461521839254693…65601409285697945599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.235 × 10⁹⁷(98-digit number)

12353461521839254693…65601409285697945601

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

2.470 × 10⁹⁷(98-digit number)

24706923043678509387…31202818571395891199

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 #280,770

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