Block #1,350,261

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2015, 10:02:49 PM · Difficulty 10.8029 · 5,460,210 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a3eabecfcb48df9a0574ba740e904b60429df1307785e72993faf1b7f2209fa9

View on Chainz ↗

Height

#1,350,261

Difficulty

10.802950

Transactions

Size

937 B

Version

Bits

0acd8e1b

Nonce

404,872,318

Timestamp

12/1/2015, 10:02:49 PM

Confirmations

5,460,210

Mined by

⛏️ P2SHAG7NemQA5KbQGEZXr5ureC4HRnECzrVVSU

Merkle Root

545c1b1244dd775e34163e1ddb8a1a66b8276c7ba17c812d7b427678efbebacf

Transactions (2)

Coinbase459ecae06a3655…ba90b02d17d3a9

1 in → 1 out8.5700 XPM110 B

AG7NemQA…ECzrVVSU

c4a7c98fde4523…3e7b2ffd0b8015

1 in → 17 out122.1184 XPM737 B

AcccHhSf…yxZnjnk6 APHM7qh3…1tz2niSm AQppDAHZ…HzsaE5ca AddXD64V…CNkqd3iD ASNueevd…k51oyWvn

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.

6.010 × 10⁹³(94-digit number)

60106679576750638452…63699166209114203999

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

6.010 × 10⁹³(94-digit number)

60106679576750638452…63699166209114203999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.010 × 10⁹³(94-digit number)

60106679576750638452…63699166209114204001

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

1.202 × 10⁹⁴(95-digit number)

12021335915350127690…27398332418228407999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.202 × 10⁹⁴(95-digit number)

12021335915350127690…27398332418228408001

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

2.404 × 10⁹⁴(95-digit number)

24042671830700255381…54796664836456815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.404 × 10⁹⁴(95-digit number)

24042671830700255381…54796664836456816001

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

4.808 × 10⁹⁴(95-digit number)

48085343661400510762…09593329672913631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.808 × 10⁹⁴(95-digit number)

48085343661400510762…09593329672913632001

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

9.617 × 10⁹⁴(95-digit number)

96170687322801021524…19186659345827263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.617 × 10⁹⁴(95-digit number)

96170687322801021524…19186659345827264001

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 #1,350,261

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