Block #364,787

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2014, 7:28:19 AM · Difficulty 10.4231 · 6,431,685 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

261bae0c1371e19fad0b4a5551f829270b409e3b9def73aaeafa4e768daf55dd

View on Chainz ↗

Height

#364,787

Difficulty

10.423128

Transactions

Size

228 B

Version

Bits

0a6c521e

Nonce

36,374

Timestamp

1/18/2014, 7:28:19 AM

Confirmations

6,431,685

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

b5aa6530619a81a551742ab193f648fe38ad6dcce18114bcd61b8b151d0f4df1

Transactions (1)

Coinbaseb5aa6530619a81…1b8b151d0f4df1

1 in → 2 out9.1900 XPM136 B

ARmAMwyu…P7Kn74ZT ALfEGCwh…VawujfMm

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.

2.355 × 10⁹⁹(100-digit number)

23559587362898170622…11992793982988403199

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

2.355 × 10⁹⁹(100-digit number)

23559587362898170622…11992793982988403199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.355 × 10⁹⁹(100-digit number)

23559587362898170622…11992793982988403201

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

4.711 × 10⁹⁹(100-digit number)

47119174725796341244…23985587965976806399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.711 × 10⁹⁹(100-digit number)

47119174725796341244…23985587965976806401

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

9.423 × 10⁹⁹(100-digit number)

94238349451592682489…47971175931953612799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.423 × 10⁹⁹(100-digit number)

94238349451592682489…47971175931953612801

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

1.884 × 10¹⁰⁰(101-digit number)

18847669890318536497…95942351863907225599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.884 × 10¹⁰⁰(101-digit number)

18847669890318536497…95942351863907225601

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

3.769 × 10¹⁰⁰(101-digit number)

37695339780637072995…91884703727814451199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.769 × 10¹⁰⁰(101-digit number)

37695339780637072995…91884703727814451201

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