Block #378,131

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2014, 2:34:15 PM · Difficulty 10.4230 · 6,420,803 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d36141ddb307d488b0d0bc70c90aa48c09e2f549ff7e0e9b0439862558331394

View on Chainz ↗

Height

#378,131

Difficulty

10.423016

Transactions

Size

1.05 KB

Version

Bits

0a6c4ac3

Nonce

101,018

Timestamp

1/27/2014, 2:34:15 PM

Confirmations

6,420,803

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

46186445d999f346c0ca207374305c7d28cc6577a50eea1e1fe7eb47cdb2a0ec

Transactions (5)

Coinbase4de3f07530e6e3…d2657c1c5f8339

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

626c422042c65e…a96c361bc380ff

1 in → 1 out9.9900 XPM192 B

AVrzKB8z…MWm9DJcx

57e493a17004a4…b6de2b1d7ccf2a

1 in → 2 out12.1164 XPM226 B

AUH8H7bo…LBL5P3tp AMzdNu2A…9cjPDmhx

6ea330dac71673…86b60707aee9ac

1 in → 2 out3.3493 XPM226 B

AN6zy2eX…MqHBSP36 AS9MQRHu…XzC8bVn6

7b0bf0e2d4edc0…b655cc1a65e601

1 in → 2 out4.0521 XPM227 B

ASGoUfHB…eDgFu5yk AQ1rjr43…JUYWeJ1n

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.

2.907 × 10¹⁰¹(102-digit number)

29078813004057173878…76370561853129743359

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

2.907 × 10¹⁰¹(102-digit number)

29078813004057173878…76370561853129743359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.907 × 10¹⁰¹(102-digit number)

29078813004057173878…76370561853129743361

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

5.815 × 10¹⁰¹(102-digit number)

58157626008114347757…52741123706259486719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.815 × 10¹⁰¹(102-digit number)

58157626008114347757…52741123706259486721

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

1.163 × 10¹⁰²(103-digit number)

11631525201622869551…05482247412518973439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.163 × 10¹⁰²(103-digit number)

11631525201622869551…05482247412518973441

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

2.326 × 10¹⁰²(103-digit number)

23263050403245739103…10964494825037946879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.326 × 10¹⁰²(103-digit number)

23263050403245739103…10964494825037946881

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

4.652 × 10¹⁰²(103-digit number)

46526100806491478206…21928989650075893759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.652 × 10¹⁰²(103-digit number)

46526100806491478206…21928989650075893761

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