Block #1,404,781

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/8/2016, 6:14:56 PM · Difficulty 10.8063 · 5,403,522 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ce4dd9731ef2d679f49cf98174c0d52234a6e380fc9061ee1943a8607363a26f

View on Chainz ↗

Height

#1,404,781

Difficulty

10.806266

Transactions

Size

3.45 KB

Version

Bits

0ace6774

Nonce

420,297,689

Timestamp

1/8/2016, 6:14:56 PM

Confirmations

5,403,522

Mined by

⛏️ P2SHAdWp4WhRKHE1qx1UBsDk4CAMirGZPhjpsn

Merkle Root

be39650414f8352965c2ecf0c758ab07cae0e2d38074975e42ac05b085b0fcf4

Transactions (4)

Coinbase673e0308b690ac…60b5831e6919ff

1 in → 1 out8.6100 XPM109 B

AdWp4WhR…GZPhjpsn

d6d0dc4d1b15e6…893e7ee868483c

1 in → 28 out287.9234 XPM1.08 KB

AJ9cg1cG…6caZy7Ld ASCVSbVk…rPaegyxe ATyHFdjS…kku74cEm AFqAiWtG…JNZAjpHt AMTQioZS…PFnpK9kE

29835bd8943045…aa02ba65cdc289

1 in → 29 out286.9866 XPM1.12 KB

AdN1cPGQ…3WtjXRtv ASTe5U9e…F3fUaqso AHrXTiGW…8HvirjKM AW2TSH7W…kWzdREtp AUf8Sixq…SUoEoccN

0d3299295cfb0e…4363f0e2e9fb1f

1 in → 27 out285.9327 XPM1.05 KB

APGdziGW…3ou8jPJi ASCVSbVk…rPaegyxe Ab7eHcAm…p5iZ6Yga AVtF3a7i…o8Hu62qE ARb2Whmi…3eQaSMW4

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.

1.662 × 10⁹⁵(96-digit number)

16629204433123447829…74665933193462295199

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

1.662 × 10⁹⁵(96-digit number)

16629204433123447829…74665933193462295199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.662 × 10⁹⁵(96-digit number)

16629204433123447829…74665933193462295201

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

3.325 × 10⁹⁵(96-digit number)

33258408866246895659…49331866386924590399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.325 × 10⁹⁵(96-digit number)

33258408866246895659…49331866386924590401

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

6.651 × 10⁹⁵(96-digit number)

66516817732493791318…98663732773849180799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.651 × 10⁹⁵(96-digit number)

66516817732493791318…98663732773849180801

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

1.330 × 10⁹⁶(97-digit number)

13303363546498758263…97327465547698361599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.330 × 10⁹⁶(97-digit number)

13303363546498758263…97327465547698361601

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

2.660 × 10⁹⁶(97-digit number)

26606727092997516527…94654931095396723199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.660 × 10⁹⁶(97-digit number)

26606727092997516527…94654931095396723201

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

5.321 × 10⁹⁶(97-digit number)

53213454185995033054…89309862190793446399

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 #1,404,781

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