Block #116,721

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/14/2013, 2:28:45 PM · Difficulty 9.7495 · 6,686,552 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

284781d61f4eb2f431c63d659e2fdcc6079fc16c9239894badcf8bb0debaa939

View on Chainz ↗

Height

#116,721

Difficulty

9.749468

Transactions

Size

1.67 KB

Version

Bits

09bfdd29

Nonce

310,729

Timestamp

8/14/2013, 2:28:45 PM

Confirmations

6,686,552

Mined by

⛏️ P2SHAWekHYhnnraHf28To1LDJWDs1rXXubSnG4

Merkle Root

378a4ea4757ebe5f22357fafd474d635b3415a0cdcec515a02e4293806f559f2

Transactions (5)

Coinbase0dff4a124d4992…d9146f39a01ba2

1 in → 1 out10.5500 XPM109 B

AWekHYhn…XXubSnG4

5d1ca7d0794b3d…638627caf82f2d

2 in → 2 out60.1065 XPM372 B

AXcca7kC…Uh7yEm7R AcWNpkXk…cRTM3N8y

ad54ea3b0800bd…886f755438287e

2 in → 2 out60.8900 XPM372 B

Ab7iXvjf…LnFwMDZn AU77a6pF…wnNTpB9q

04016ecab82d6e…00ed7063b1ebb1

4 in → 2 out42.2600 XPM534 B

ATfwKEAp…rViFgg4S AHnvJDiF…j8QVpNpY

95d818b945ba7c…93817ca75ff8ea

1 in → 2 out6.4551 XPM227 B

AG7p81H8…XV9eBHrh AZaTgNp4…wEYWkGS2

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.

4.709 × 10⁹⁶(97-digit number)

47094615632245517701…42980193634278436379

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

4.709 × 10⁹⁶(97-digit number)

47094615632245517701…42980193634278436379

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.709 × 10⁹⁶(97-digit number)

47094615632245517701…42980193634278436381

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

9.418 × 10⁹⁶(97-digit number)

94189231264491035402…85960387268556872759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.418 × 10⁹⁶(97-digit number)

94189231264491035402…85960387268556872761

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

1.883 × 10⁹⁷(98-digit number)

18837846252898207080…71920774537113745519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.883 × 10⁹⁷(98-digit number)

18837846252898207080…71920774537113745521

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

3.767 × 10⁹⁷(98-digit number)

37675692505796414160…43841549074227491039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.767 × 10⁹⁷(98-digit number)

37675692505796414160…43841549074227491041

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

7.535 × 10⁹⁷(98-digit number)

75351385011592828321…87683098148454982079

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