Block #73,152

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 4:15:06 AM · Difficulty 8.9946 · 6,719,536 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

89f86f7c982b4622dbbefd14a75c367d146ee0d2ec04e41b7cb34afef34f9708

View on Chainz ↗

Height

#73,152

Difficulty

8.994616

Transactions

Size

2.03 KB

Version

Bits

08fe9f26

Nonce

303

Timestamp

7/21/2013, 4:15:06 AM

Confirmations

6,719,536

Merkle Root

4461bee132250e7068d82c79e19987553f8c3f260b120ff5d0e79de54f508e4b

Transactions (2)

Coinbase652f89671db4f2…e91eb305e3809f

1 in → 1 out12.3600 XPM110 B

AZertJFJ…wGtTKrE9

8abe37708874f3…f3ef9120eaac95

16 in → 1 out197.6200 XPM1.83 KB

AakWTnji…NVBZri5U

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.

1.276 × 10¹⁰⁰(101-digit number)

12761358328616556445…92313554594256716939

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

1.276 × 10¹⁰⁰(101-digit number)

12761358328616556445…92313554594256716939

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.276 × 10¹⁰⁰(101-digit number)

12761358328616556445…92313554594256716941

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

2.552 × 10¹⁰⁰(101-digit number)

25522716657233112890…84627109188513433879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.552 × 10¹⁰⁰(101-digit number)

25522716657233112890…84627109188513433881

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

5.104 × 10¹⁰⁰(101-digit number)

51045433314466225781…69254218377026867759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.104 × 10¹⁰⁰(101-digit number)

51045433314466225781…69254218377026867761

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

1.020 × 10¹⁰¹(102-digit number)

10209086662893245156…38508436754053735519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.020 × 10¹⁰¹(102-digit number)

10209086662893245156…38508436754053735521

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

2.041 × 10¹⁰¹(102-digit number)

20418173325786490312…77016873508107471039

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