Block #365,732

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2014, 11:11:06 PM · Difficulty 10.4241 · 6,445,338 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d286db96093b0f06c03b376cd0cb3661411e6f6fe75d9fe13b94b7063cce018d

View on Chainz ↗

Height

#365,732

Difficulty

10.424109

Transactions

Size

455 B

Version

Bits

0a6c926a

Nonce

45,196

Timestamp

1/18/2014, 11:11:06 PM

Confirmations

6,445,338

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

97fee7ca5ba2d1a40a2dde94a8483b4ff6f7d1771b4243e185886648c75c58da

Transactions (2)

Coinbase4e558ff3f3310b…3db512c49728ec

1 in → 2 out9.2100 XPM136 B

ARmAMwyu…P7Kn74ZT AU6kq4CL…dQBLvxLp

420ddcb4d84fcd…8b8adc8edff4c3

1 in → 2 out0.2900 XPM226 B

AbbFD9As…8Qy9wDvg AVP53GXA…yb9MA2yX

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.

1.108 × 10¹⁰¹(102-digit number)

11089240139602370915…41625978294852794879

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

1.108 × 10¹⁰¹(102-digit number)

11089240139602370915…41625978294852794879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.108 × 10¹⁰¹(102-digit number)

11089240139602370915…41625978294852794881

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

2.217 × 10¹⁰¹(102-digit number)

22178480279204741831…83251956589705589759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.217 × 10¹⁰¹(102-digit number)

22178480279204741831…83251956589705589761

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

4.435 × 10¹⁰¹(102-digit number)

44356960558409483663…66503913179411179519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.435 × 10¹⁰¹(102-digit number)

44356960558409483663…66503913179411179521

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

8.871 × 10¹⁰¹(102-digit number)

88713921116818967327…33007826358822359039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.871 × 10¹⁰¹(102-digit number)

88713921116818967327…33007826358822359041

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

1.774 × 10¹⁰²(103-digit number)

17742784223363793465…66015652717644718079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.774 × 10¹⁰²(103-digit number)

17742784223363793465…66015652717644718081

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 #365,732

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