Block #420,938

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/26/2014, 5:02:23 PM · Difficulty 10.3754 · 6,373,331 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b5ff942ead75918c166345b812c5ab0f9008924b483b2a6f3ef292135df91fcb

View on Chainz ↗

Height

#420,938

Difficulty

10.375369

Transactions

Size

59.63 KB

Version

Bits

0a601830

Nonce

17,148

Timestamp

2/26/2014, 5:02:23 PM

Confirmations

6,373,331

Merkle Root

3eed8f865f6ff38d859fe9b92735316d19d8923e314b0c8e428b6b451e41d587

Transactions (3)

Coinbase9dc09157d70c4a…e943dae66558fa

1 in → 1 out9.9000 XPM109 B

ARGDpaX1…jdDV6Zxb

eb264446c312ea…e33ba37bd69ab4

409 in → 2 out419.4068 XPM59.21 KB

AYXe29zr…LHD2DAFN APEFyvvz…7JYgHaWM

48ee36fd1071db…ba05d79a284968

1 in → 2 out5.1297 XPM226 B

AHksUkWQ…geieEwPK AQVQdkmm…iNK1T9mT

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.

9.706 × 10⁹⁹(100-digit number)

97061092308561730860…87269949970459815679

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

9.706 × 10⁹⁹(100-digit number)

97061092308561730860…87269949970459815679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.706 × 10⁹⁹(100-digit number)

97061092308561730860…87269949970459815681

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

1.941 × 10¹⁰⁰(101-digit number)

19412218461712346172…74539899940919631359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.941 × 10¹⁰⁰(101-digit number)

19412218461712346172…74539899940919631361

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

3.882 × 10¹⁰⁰(101-digit number)

38824436923424692344…49079799881839262719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.882 × 10¹⁰⁰(101-digit number)

38824436923424692344…49079799881839262721

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

7.764 × 10¹⁰⁰(101-digit number)

77648873846849384688…98159599763678525439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.764 × 10¹⁰⁰(101-digit number)

77648873846849384688…98159599763678525441

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

1.552 × 10¹⁰¹(102-digit number)

15529774769369876937…96319199527357050879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.552 × 10¹⁰¹(102-digit number)

15529774769369876937…96319199527357050881

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