Block #260,650

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/14/2013, 1:51:59 PM · Difficulty 9.9767 · 6,557,163 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

003828e8f7e686f7a3d9393a34ca62ee9a946affc0d274ca554f1b296fcf031d

View on Chainz ↗

Height

#260,650

Difficulty

9.976669

Transactions

Size

1.15 KB

Version

Bits

09fa0703

Nonce

169,066

Timestamp

11/14/2013, 1:51:59 PM

Confirmations

6,557,163

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

7bdde49e3be9d90771e4d57f44ec4b0ec30556c6f59e54dce538c4ef0189a75d

Transactions (4)

Coinbasebbd4d719797c8e…fa3d7d4144d18a

1 in → 1 out10.0600 XPM110 B

AeKNrjNj…1NEq95Ta

33bd887462ac61…b0f9fb350e2d2a

3 in → 2 out13.9154 XPM523 B

ALiSLa7G…cgYVh7Lc AG63TF4Z…XbHtbs5G

88f1f10dac5004…0cac0a00294d3d

1 in → 4 out10.0200 XPM259 B

AWAmfRKG…Fk7UXape AbJAcEfw…PkVprLzT AcADmAoe…8iNnoMzB AeKNrjNj…1NEq95Ta

a6efc862bc50c0…28e90f3ae7cb44

1 in → 1 out3.0001 XPM192 B

APqd3RiR…sduuPdAZ

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.

7.292 × 10⁹⁴(95-digit number)

72923588360576631336…92960532700166431349

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

7.292 × 10⁹⁴(95-digit number)

72923588360576631336…92960532700166431349

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.292 × 10⁹⁴(95-digit number)

72923588360576631336…92960532700166431351

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

1.458 × 10⁹⁵(96-digit number)

14584717672115326267…85921065400332862699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.458 × 10⁹⁵(96-digit number)

14584717672115326267…85921065400332862701

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

2.916 × 10⁹⁵(96-digit number)

29169435344230652534…71842130800665725399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.916 × 10⁹⁵(96-digit number)

29169435344230652534…71842130800665725401

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

5.833 × 10⁹⁵(96-digit number)

58338870688461305069…43684261601331450799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.833 × 10⁹⁵(96-digit number)

58338870688461305069…43684261601331450801

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

1.166 × 10⁹⁶(97-digit number)

11667774137692261013…87368523202662901599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.166 × 10⁹⁶(97-digit number)

11667774137692261013…87368523202662901601

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

Block #260,650

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