Block #681,949

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/17/2014, 9:53:23 PM · Difficulty 10.9611 · 6,121,376 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4856c0d2ee88f297833a7e14d42c15e0c56bc2162f89a1e8ed070f2711f56619

View on Chainz ↗

Height

#681,949

Difficulty

10.961097

Transactions

Size

1.43 KB

Version

Bits

0af60a73

Nonce

235,753,714

Timestamp

8/17/2014, 9:53:23 PM

Confirmations

6,121,376

Mined by

⛏️ P2SHAULY2pjcxaZL8LG72BvVyaaH2AephkB2qi

Merkle Root

6fdc8a7f07194d5220304bee0e960a9b8389bb1865c5c5127434d9e12effe4e4

Transactions (4)

Coinbase59305ba9c9af0e…40949726563ef3

1 in → 1 out8.3500 XPM109 B

AULY2pjc…ephkB2qi

1766774c41249b…174e72ea38d197

5 in → 2 out8.1947 XPM814 B

AVuHjVnu…8nVBBise AbhKqSkh…2PRPrSEp

0884cfb85da4bc…20635afd7aaa55

1 in → 2 out7.2713 XPM227 B

AZqmL7F2…vY7GxDHr AXE5jfMX…JVwA3M4h

1e127b05e4df6a…7fc5a368cc9e59

1 in → 2 out1.1945 XPM227 B

AX8JLXVZ…XsZWwnhw Abs1CTRR…uk6ieBYF

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.

2.830 × 10⁹⁶(97-digit number)

28308529880611211070…17223936063009013759

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

2.830 × 10⁹⁶(97-digit number)

28308529880611211070…17223936063009013759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.830 × 10⁹⁶(97-digit number)

28308529880611211070…17223936063009013761

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

5.661 × 10⁹⁶(97-digit number)

56617059761222422140…34447872126018027519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.661 × 10⁹⁶(97-digit number)

56617059761222422140…34447872126018027521

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

1.132 × 10⁹⁷(98-digit number)

11323411952244484428…68895744252036055039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.132 × 10⁹⁷(98-digit number)

11323411952244484428…68895744252036055041

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

2.264 × 10⁹⁷(98-digit number)

22646823904488968856…37791488504072110079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.264 × 10⁹⁷(98-digit number)

22646823904488968856…37791488504072110081

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

4.529 × 10⁹⁷(98-digit number)

45293647808977937712…75582977008144220159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.529 × 10⁹⁷(98-digit number)

45293647808977937712…75582977008144220161

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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