Block #81,303

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 4:07:45 PM · Difficulty 9.2694 · 6,709,638 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de7b059df8c1900dd79b9e958f4494c5a6122afdcb28df3b3b3c218ab0b597fc

View on Chainz ↗

Height

#81,303

Difficulty

9.269448

Transactions

Size

1.43 KB

Version

Bits

0944fa86

Nonce

106,493

Timestamp

7/24/2013, 4:07:45 PM

Confirmations

6,709,638

Merkle Root

d0dbe78db0df8d33c2f258b76e6283f0541fe1e1c1dec7f3294ddb77171f02fe

Transactions (4)

Coinbase5ed1e59c321a86…fefb8f14fa2c35

1 in → 1 out11.6500 XPM109 B

AaJYWZbd…5JYgjaRM

ca2ddd1352721e…1e176ce9ae4757

2 in → 2 out211.9300 XPM374 B

AYCDoGAE…WjLvE65q AS2iwQSB…mttFaj2Q

7a2171b0357e64…b9716447d69468

6 in → 1 out71.3800 XPM731 B

AJbRq3bT…WTZ3C1Wz

c5e5b811e12c7c…da377c5e3beaa2

1 in → 1 out11.7600 XPM158 B

AdJbSNCM…VdXUWZw8

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.

6.894 × 10⁹²(93-digit number)

68944422350922798041…13044697735707347549

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

6.894 × 10⁹²(93-digit number)

68944422350922798041…13044697735707347549

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.894 × 10⁹²(93-digit number)

68944422350922798041…13044697735707347551

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

1.378 × 10⁹³(94-digit number)

13788884470184559608…26089395471414695099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.378 × 10⁹³(94-digit number)

13788884470184559608…26089395471414695101

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

2.757 × 10⁹³(94-digit number)

27577768940369119216…52178790942829390199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.757 × 10⁹³(94-digit number)

27577768940369119216…52178790942829390201

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

5.515 × 10⁹³(94-digit number)

55155537880738238433…04357581885658780399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.515 × 10⁹³(94-digit number)

55155537880738238433…04357581885658780401

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

1.103 × 10⁹⁴(95-digit number)

11031107576147647686…08715163771317560799

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