Block #958,408

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2015, 11:09:30 AM · Difficulty 10.8893 · 5,847,760 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3781605aeb2ee02cdf9ca9b37fdde59331c5f6f24b4e73e89301a8be2f51f4c8

View on Chainz ↗

Height

#958,408

Difficulty

10.889256

Transactions

Size

2.53 KB

Version

Bits

0ae3a643

Nonce

814,169,021

Timestamp

3/2/2015, 11:09:30 AM

Confirmations

5,847,760

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

70b13416b135e5a135b33f7fefe09bbd9e666a92f31bc9d5e1b0e36c92e90e51

Transactions (5)

Coinbaseb83f88ccc5f892…7f3d757692e4e0

1 in → 1 out8.4700 XPM116 B

ANSXnLY2…Sd25TjkD

c55c028957d983…8e26f407cd8146

9 in → 2 out1537.2836 XPM1.38 KB

APKirZWi…NTdN7ZTc AKG9kghn…g8DsAdAw

3cea7c9be3b716…04ca2f9c76a652

2 in → 2 out16.8100 XPM374 B

AGY8b93t…deokYRcA ATDzT9Qg…xPgwgjb1

7f8beb34cbe892…e29b7e9ec00d2d

2 in → 2 out16.1400 XPM373 B

AXSi9Tes…STgog5gB AR1UBmRh…Xn78q4ZQ

a22eee17e7ab59…c71c2258f9d6bb

1 in → 2 out2.0657 XPM225 B

ANfmUrFA…kVSzdPqM ALX4Yiea…g71AQ3vj

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.

3.328 × 10⁹⁷(98-digit number)

33280785623709007189…75814683848129704959

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

3.328 × 10⁹⁷(98-digit number)

33280785623709007189…75814683848129704959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.328 × 10⁹⁷(98-digit number)

33280785623709007189…75814683848129704961

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

6.656 × 10⁹⁷(98-digit number)

66561571247418014378…51629367696259409919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.656 × 10⁹⁷(98-digit number)

66561571247418014378…51629367696259409921

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

1.331 × 10⁹⁸(99-digit number)

13312314249483602875…03258735392518819839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.331 × 10⁹⁸(99-digit number)

13312314249483602875…03258735392518819841

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

2.662 × 10⁹⁸(99-digit number)

26624628498967205751…06517470785037639679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.662 × 10⁹⁸(99-digit number)

26624628498967205751…06517470785037639681

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

5.324 × 10⁹⁸(99-digit number)

53249256997934411502…13034941570075279359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.324 × 10⁹⁸(99-digit number)

53249256997934411502…13034941570075279361

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