Block #422,088

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 11:44:40 AM · Difficulty 10.3791 · 6,387,626 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

948e16f92a7324caf75620f847b7760adf0800e5ffa40e49eb6e04d87e07257a

View on Chainz ↗

Height

#422,088

Difficulty

10.379073

Transactions

Size

1.61 KB

Version

Bits

0a610af4

Nonce

14,031

Timestamp

2/27/2014, 11:44:40 AM

Confirmations

6,387,626

Mined by

⛏️ paS%AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

826075ecfe437e1b7ebc76fbed7eec7a5aee4ba6cb445fe413fed380f829a09a

Transactions (4)

Coinbasee2ee3d291dc133…1dd5d9cabd6fc7

1 in → 24 out9.2700 XPM879 B

AQvZBsUo…hppgRZTJ AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH

0ccf302eb16a69…dbcde469798eb7

1 in → 2 out8.1497 XPM226 B

ALXa1oKc…rwjzvEVp AdVgRx9N…BmpptzYp

0a9effac0910eb…4b4adc40b6cf14

1 in → 2 out7.8411 XPM227 B

ARQokPVT…Y8r4wov9 AJvy544r…SdGaJvHg

88a02fed99cfc2…1b2fe1a006ef44

1 in → 2 out7.1985 XPM225 B

AQsqCMcB…YxgrjJnb AbX8fndo…cb4wvEoX

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.

1.534 × 10⁹⁹(100-digit number)

15344718118998863881…04785892494185973759

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

1.534 × 10⁹⁹(100-digit number)

15344718118998863881…04785892494185973759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.534 × 10⁹⁹(100-digit number)

15344718118998863881…04785892494185973761

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

3.068 × 10⁹⁹(100-digit number)

30689436237997727763…09571784988371947519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.068 × 10⁹⁹(100-digit number)

30689436237997727763…09571784988371947521

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

6.137 × 10⁹⁹(100-digit number)

61378872475995455527…19143569976743895039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.137 × 10⁹⁹(100-digit number)

61378872475995455527…19143569976743895041

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

1.227 × 10¹⁰⁰(101-digit number)

12275774495199091105…38287139953487790079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.227 × 10¹⁰⁰(101-digit number)

12275774495199091105…38287139953487790081

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

2.455 × 10¹⁰⁰(101-digit number)

24551548990398182210…76574279906975580159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.455 × 10¹⁰⁰(101-digit number)

24551548990398182210…76574279906975580161

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 #422,088

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