Block #281,677

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 2:54:13 AM · Difficulty 9.9775 · 6,523,429 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40b9fbf0b832903a770758783c1d32c29122d77c3bae240e65d82e3521c73b04

View on Chainz ↗

Height

#281,677

Difficulty

9.977526

Transactions

Size

1.01 KB

Version

Bits

09fa3f27

Nonce

6,378

Timestamp

11/29/2013, 2:54:13 AM

Confirmations

6,523,429

Mined by

⛏️ MLaRAYckRkCFgTH4MEfpDbaimvV5cSTgDe5VSp

Merkle Root

861842bdd18c3ccf1aa81008fca2aae26a0bcfc5449624fc6be3746d6473537d

Transactions (1)

Coinbase861842bdd18c3c…e3746d6473537d

1 in → 26 out10.0300 XPM947 B

AYckRkCF…TgDe5VSp Ac6mGvmQ…XqWmPHjR AbtgNzNb…9Atvu81w AZxfJPuB…prEg2B2i Ab2MXwKw…VMrmfDuo

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.

2.976 × 10⁹⁴(95-digit number)

29768104779366398691…81237314462753439999

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

2.976 × 10⁹⁴(95-digit number)

29768104779366398691…81237314462753439999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.976 × 10⁹⁴(95-digit number)

29768104779366398691…81237314462753440001

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

5.953 × 10⁹⁴(95-digit number)

59536209558732797382…62474628925506879999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.953 × 10⁹⁴(95-digit number)

59536209558732797382…62474628925506880001

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

1.190 × 10⁹⁵(96-digit number)

11907241911746559476…24949257851013759999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.190 × 10⁹⁵(96-digit number)

11907241911746559476…24949257851013760001

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

2.381 × 10⁹⁵(96-digit number)

23814483823493118952…49898515702027519999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.381 × 10⁹⁵(96-digit number)

23814483823493118952…49898515702027520001

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

4.762 × 10⁹⁵(96-digit number)

47628967646986237905…99797031404055039999

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