Block #359,849

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/15/2014, 1:58:36 AM · Difficulty 10.3874 · 6,464,932 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

91cf77da0234b5e540acf0f640d6aa28abb9af1d30efc57a2d61512be0b1fc9d

View on Chainz ↗

Height

#359,849

Difficulty

10.387438

Transactions

Size

1.08 KB

Version

Bits

0a632f29

Nonce

31,913

Timestamp

1/15/2014, 1:58:36 AM

Confirmations

6,464,932

Mined by

⛏️ P2SHAbLD75y38X9FNifbrPeN9ZJ89WtVJwYoxa

Merkle Root

803ea036874d489ee5f0e83cc8394bf654552b7fc5b4cdda049154d1d3f831dd

Transactions (5)

Coinbase941c8907f4a6a2…d7ae33ab564e79

1 in → 1 out9.2900 XPM109 B

AbLD75y3…tVJwYoxa

cbcacfb48df3f3…978b8e73ff8008

1 in → 2 out8.2365 XPM226 B

ARpTWjTM…Ca621qhU AVrEkjps…Kocgb9vD

60d692d0a7167f…bfb51995934855

1 in → 2 out5.6429 XPM225 B

AMh5hmyX…TqiKWXyH AbmJks6D…VmAfbLEQ

46299bdfb923f4…bd89c6a7bdac3c

1 in → 2 out6.2135 XPM226 B

AeRRvH1x…1ExW33LA ARRZ7oBg…4rpsBbq8

b9abaf2a0c64c4…50eac394627dbf

1 in → 2 out3.4899 XPM226 B

AUq6f9hu…XXF5HtBq AWRMwWmV…KEu6bBvz

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.

9.759 × 10¹⁰²(103-digit number)

97595061383934057656…37494439482846659199

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

9.759 × 10¹⁰²(103-digit number)

97595061383934057656…37494439482846659199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.759 × 10¹⁰²(103-digit number)

97595061383934057656…37494439482846659201

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

1.951 × 10¹⁰³(104-digit number)

19519012276786811531…74988878965693318399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.951 × 10¹⁰³(104-digit number)

19519012276786811531…74988878965693318401

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

3.903 × 10¹⁰³(104-digit number)

39038024553573623062…49977757931386636799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.903 × 10¹⁰³(104-digit number)

39038024553573623062…49977757931386636801

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

7.807 × 10¹⁰³(104-digit number)

78076049107147246125…99955515862773273599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.807 × 10¹⁰³(104-digit number)

78076049107147246125…99955515862773273601

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

1.561 × 10¹⁰⁴(105-digit number)

15615209821429449225…99911031725546547199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.561 × 10¹⁰⁴(105-digit number)

15615209821429449225…99911031725546547201

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 #359,849

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