Block #367,676

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2014, 6:20:03 AM · Difficulty 10.4332 · 6,428,143 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ed241377561b2a02f2043465c19067415aac11171df92d17a2ca3a5dfedd9146

View on Chainz ↗

Height

#367,676

Difficulty

10.433178

Transactions

Size

2.03 KB

Version

Bits

0a6ee4ba

Nonce

160,208

Timestamp

1/20/2014, 6:20:03 AM

Confirmations

6,428,143

Mined by

⛏️ <aR^AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c17de23a9b7370474fe42013e8068d793ef6e58fa98d31c64bfba36e3d72ca16

Transactions (2)

Coinbasec5af2025e0a70d…5eed020ff4ad7e

1 in → 24 out9.1700 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz AZV4TwxQ…8JnQqSoH

0c5a27d7cc34db…3ced4f89166f14

7 in → 2 out82.0100 XPM1.08 KB

APBGqsTn…6L3d9eNn AUDhSPtM…mHVCCKNj

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.

3.199 × 10⁹⁶(97-digit number)

31996264559156053766…70460040061399675519

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

3.199 × 10⁹⁶(97-digit number)

31996264559156053766…70460040061399675519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.199 × 10⁹⁶(97-digit number)

31996264559156053766…70460040061399675521

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

6.399 × 10⁹⁶(97-digit number)

63992529118312107532…40920080122799351039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.399 × 10⁹⁶(97-digit number)

63992529118312107532…40920080122799351041

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

1.279 × 10⁹⁷(98-digit number)

12798505823662421506…81840160245598702079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.279 × 10⁹⁷(98-digit number)

12798505823662421506…81840160245598702081

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

2.559 × 10⁹⁷(98-digit number)

25597011647324843012…63680320491197404159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.559 × 10⁹⁷(98-digit number)

25597011647324843012…63680320491197404161

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

5.119 × 10⁹⁷(98-digit number)

51194023294649686025…27360640982394808319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.119 × 10⁹⁷(98-digit number)

51194023294649686025…27360640982394808321

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