Block #801,639

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/7/2014, 6:50:41 PM · Difficulty 10.9761 · 6,004,603 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

88a580424ed4e5f572f775c19214d6955e33b4f02454bb5cbcedfb8629d7d8a4

View on Chainz ↗

Height

#801,639

Difficulty

10.976086

Transactions

Size

1.20 KB

Version

Bits

0af9e0cb

Nonce

2,093,809,443

Timestamp

11/7/2014, 6:50:41 PM

Confirmations

6,004,603

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d58d9b8f03a94d51fb2b8bad154a79644517eb44bb0b4ba4c1ac90040382de16

Transactions (5)

Coinbaseb28b7685296523…ac47d2b49e7baf

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

41653acf881121…39e3d37d0cc77e

2 in → 1 out699.9000 XPM340 B

AQUC7Hue…LL2XMoNY

55dd2c3b4d2c26…1f897992fbdc42

1 in → 2 out7.2535 XPM225 B

AUyLgeHT…KXTppFd9 ARpjHv1k…4F9NvuWN

3201b058d34b0e…cabfbe4d8fd1e1

1 in → 2 out7.2646 XPM226 B

AGdWVjRk…LFVsqCnK ANYowJVE…jc2mpZp9

90d1374f283ea0…7df0eeea77af0c

1 in → 2 out2.0216 XPM227 B

ALKAWKnh…EWTyqmKU ASx9RPHT…8fVzc2Ey

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.

3.003 × 10⁹⁹(100-digit number)

30039258237510031299…71443984984396267519

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

3.003 × 10⁹⁹(100-digit number)

30039258237510031299…71443984984396267519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.003 × 10⁹⁹(100-digit number)

30039258237510031299…71443984984396267521

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

6.007 × 10⁹⁹(100-digit number)

60078516475020062599…42887969968792535039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.007 × 10⁹⁹(100-digit number)

60078516475020062599…42887969968792535041

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

1.201 × 10¹⁰⁰(101-digit number)

12015703295004012519…85775939937585070079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.201 × 10¹⁰⁰(101-digit number)

12015703295004012519…85775939937585070081

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

2.403 × 10¹⁰⁰(101-digit number)

24031406590008025039…71551879875170140159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.403 × 10¹⁰⁰(101-digit number)

24031406590008025039…71551879875170140161

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

4.806 × 10¹⁰⁰(101-digit number)

48062813180016050079…43103759750340280319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.806 × 10¹⁰⁰(101-digit number)

48062813180016050079…43103759750340280321

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

Block #801,639

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