Block #676,888

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/14/2014, 12:46:20 AM · Difficulty 10.9648 · 6,118,994 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a16a95ac88b8009acb87174f62806ef0c3f6144b0d90582bff296f26f9e60913

View on Chainz ↗

Height

#676,888

Difficulty

10.964791

Transactions

Size

1.37 KB

Version

Bits

0af6fc8a

Nonce

964,328,554

Timestamp

8/14/2014, 12:46:20 AM

Confirmations

6,118,994

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5e9a1cde3079a38ed9391128b12f76cf38de5ab72156b0405dce18e1f1ad09d9

Transactions (5)

Coinbase1ea83d9bcaf6f2…5c683ca800eeb3

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

68eac7b7cc42bd…6a0c0680b7535f

2 in → 2 out11.3085 XPM374 B

ALe73byb…gZoPcGoS AXXrfFT1…6RLAGabU

91aa29b2bba153…37204acd42a0ba

2 in → 2 out11.5627 XPM373 B

AbF6QX94…7RpjqoNm AX2bVAtJ…GpaxY2ja

12e56edfdc52b5…87ae6a60757d6d

1 in → 2 out6.1614 XPM225 B

Ad1cDwwS…X59nfKas AXMgs6aY…XVs3zYEq

3a22f90b6d05af…11ea215f0b716b

1 in → 2 out6.1081 XPM227 B

AcKerPva…qeeuPChG AGZ5drdg…5ZQgZRRC

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.

1.031 × 10⁹⁷(98-digit number)

10317251367892733026…82604016028285183999

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

1.031 × 10⁹⁷(98-digit number)

10317251367892733026…82604016028285183999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.031 × 10⁹⁷(98-digit number)

10317251367892733026…82604016028285184001

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

2.063 × 10⁹⁷(98-digit number)

20634502735785466053…65208032056570367999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.063 × 10⁹⁷(98-digit number)

20634502735785466053…65208032056570368001

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

4.126 × 10⁹⁷(98-digit number)

41269005471570932106…30416064113140735999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.126 × 10⁹⁷(98-digit number)

41269005471570932106…30416064113140736001

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

8.253 × 10⁹⁷(98-digit number)

82538010943141864213…60832128226281471999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.253 × 10⁹⁷(98-digit number)

82538010943141864213…60832128226281472001

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

1.650 × 10⁹⁸(99-digit number)

16507602188628372842…21664256452562943999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.650 × 10⁹⁸(99-digit number)

16507602188628372842…21664256452562944001

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

3.301 × 10⁹⁸(99-digit number)

33015204377256745685…43328512905125887999

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