Block #509,651

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/25/2014, 4:49:32 AM · Difficulty 10.8206 · 6,283,372 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8317f52ebf0977af34682a7de1755d8263da476694b8286fd0d177ba869a191e

View on Chainz ↗

Height

#509,651

Difficulty

10.820579

Transactions

Size

697 B

Version

Bits

0ad21179

Nonce

223,561

Timestamp

4/25/2014, 4:49:32 AM

Confirmations

6,283,372

Merkle Root

2a6827fe80f903a093449f00f83926dce8855bc3955c5651c2c1863ce9b3ac8d

Transactions (1)

Coinbase2a6827fe80f903…c1863ce9b3ac8d

1 in → 16 out8.5300 XPM607 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf ATKK7iFz…wZm46KN1

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.

1.687 × 10⁹⁵(96-digit number)

16873610958618194657…06799356930457160499

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

1.687 × 10⁹⁵(96-digit number)

16873610958618194657…06799356930457160499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.687 × 10⁹⁵(96-digit number)

16873610958618194657…06799356930457160501

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

3.374 × 10⁹⁵(96-digit number)

33747221917236389314…13598713860914320999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.374 × 10⁹⁵(96-digit number)

33747221917236389314…13598713860914321001

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

6.749 × 10⁹⁵(96-digit number)

67494443834472778629…27197427721828641999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.749 × 10⁹⁵(96-digit number)

67494443834472778629…27197427721828642001

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

1.349 × 10⁹⁶(97-digit number)

13498888766894555725…54394855443657283999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.349 × 10⁹⁶(97-digit number)

13498888766894555725…54394855443657284001

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

2.699 × 10⁹⁶(97-digit number)

26997777533789111451…08789710887314567999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.699 × 10⁹⁶(97-digit number)

26997777533789111451…08789710887314568001

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

5.399 × 10⁹⁶(97-digit number)

53995555067578222903…17579421774629135999

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