Block #808,974

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/13/2014, 6:25:34 AM · Difficulty 10.9735 · 6,036,417 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d956324f1c402519ef0c0ba5b55a890b8617dc295c9398345bad9f94deaf24de

View on Chainz ↗

Height

#808,974

Difficulty

10.973515

Transactions

Size

884 B

Version

Bits

0af93846

Nonce

1,392,187,927

Timestamp

11/13/2014, 6:25:34 AM

Confirmations

6,036,417

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ac8656c3832d2f74b3341e8c12ac3ebed30bb6972c5a455183c2da9a8a555d62

Transactions (4)

Coinbase6048034df04b8f…47d39f8b0e3d9f

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

8e07af505d2631…aeeac3fc5b06b6

1 in → 2 out8.2800 XPM226 B

AMTvqX3a…sxpwNFyf AXEa1nsm…93u4jWmQ

652ae96d2e2665…83267f198629cf

1 in → 2 out7.7648 XPM226 B

AMJnih92…f3UgS2ct AbBXEaL7…UviJsPiU

83bb842c17b796…e3d5d2d43571e8

1 in → 2 out6.9206 XPM225 B

AVDyn2RZ…q5g21Mdv Aa4PtTwK…H3ppZFzk

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.

8.019 × 10⁹⁵(96-digit number)

80196516861792358214…04653609503579048959

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

8.019 × 10⁹⁵(96-digit number)

80196516861792358214…04653609503579048959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.019 × 10⁹⁵(96-digit number)

80196516861792358214…04653609503579048961

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

1.603 × 10⁹⁶(97-digit number)

16039303372358471642…09307219007158097919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.603 × 10⁹⁶(97-digit number)

16039303372358471642…09307219007158097921

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

3.207 × 10⁹⁶(97-digit number)

32078606744716943285…18614438014316195839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.207 × 10⁹⁶(97-digit number)

32078606744716943285…18614438014316195841

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

6.415 × 10⁹⁶(97-digit number)

64157213489433886571…37228876028632391679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.415 × 10⁹⁶(97-digit number)

64157213489433886571…37228876028632391681

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

1.283 × 10⁹⁷(98-digit number)

12831442697886777314…74457752057264783359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.283 × 10⁹⁷(98-digit number)

12831442697886777314…74457752057264783361

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

2.566 × 10⁹⁷(98-digit number)

25662885395773554628…48915504114529566719

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

Block #808,974

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