Block #762,090

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/11/2014, 8:50:06 AM · Difficulty 10.9744 · 6,043,970 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

413c6c7d47e9fff48e75cc2d19c58694c235063c7801a900ac9da724c069e33a

View on Chainz ↗

Height

#762,090

Difficulty

10.974367

Transactions

Size

2.10 KB

Version

Bits

0af97023

Nonce

5,083,502

Timestamp

10/11/2014, 8:50:06 AM

Confirmations

6,043,970

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

61496cc3891ec57936f4ab58ff3d31f5405d94899a19a3f05d78b8d1082b9490

Transactions (5)

Coinbase845dbc66f4a63a…af5533dcbbc106

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

d6bc80ad5a848d…a5a70ed03d6a15

7 in → 2 out50.0466 XPM1.09 KB

ANxBNgkB…9KDzRP6s AbUCnoSf…2TQRniBZ

4483513eae0cc8…778fa6ace702cf

2 in → 2 out12.1356 XPM373 B

ANnPabNH…tUvXAmek AU9mPKZv…jZiYTZsR

94877fd77e54b9…61e594e785fb70

1 in → 2 out5.6677 XPM226 B

AYFxzicp…jeAdgy2P AFrAkksp…T2eLNHrn

e8e8ccc07fa015…145c8d2303d9fc

1 in → 2 out1.1281 XPM225 B

AMx9mTdJ…UwM1tSSA AegeMkJx…SoKpjbJB

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.

1.176 × 10⁹⁹(100-digit number)

11766706031994931707…41358873708224716799

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

1.176 × 10⁹⁹(100-digit number)

11766706031994931707…41358873708224716799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.176 × 10⁹⁹(100-digit number)

11766706031994931707…41358873708224716801

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

2.353 × 10⁹⁹(100-digit number)

23533412063989863414…82717747416449433599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.353 × 10⁹⁹(100-digit number)

23533412063989863414…82717747416449433601

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

4.706 × 10⁹⁹(100-digit number)

47066824127979726829…65435494832898867199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.706 × 10⁹⁹(100-digit number)

47066824127979726829…65435494832898867201

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

9.413 × 10⁹⁹(100-digit number)

94133648255959453659…30870989665797734399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.413 × 10⁹⁹(100-digit number)

94133648255959453659…30870989665797734401

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

1.882 × 10¹⁰⁰(101-digit number)

18826729651191890731…61741979331595468799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.882 × 10¹⁰⁰(101-digit number)

18826729651191890731…61741979331595468801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.765 × 10¹⁰⁰(101-digit number)

37653459302383781463…23483958663190937599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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