Block #791,112

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/31/2014, 7:51:12 PM · Difficulty 10.9732 · 6,014,058 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

39d239f0f55dd6be972290cc6e0991e3397620374e3040b16f4b838b193570b1

View on Chainz ↗

Height

#791,112

Difficulty

10.973198

Transactions

Size

851 B

Version

Bits

0af92383

Nonce

1,282,317,433

Timestamp

10/31/2014, 7:51:12 PM

Confirmations

6,014,058

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1139cf2bbb2cea6662ff8d5d7a2ec9435b493c5874a2b32425e6a3632ef75f89

Transactions (4)

Coinbaseffacd17f82537c…fcaf76c04b07ef

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

714e643aa9af8a…ab4f92e3887c60

1 in → 2 out8.3600 XPM192 B

AQhxtjDh…2Y6kgB9F ANbzzDzN…kruPd3k8

90f0b834c8c561…76c37a8c2c783a

1 in → 2 out5.6350 XPM227 B

AWmTZUce…P28DV9Jv AREmLC5L…3hsWg33i

7c1fe4daa53228…faa227f299ad66

1 in → 2 out0.8520 XPM226 B

AMoJsji6…a13Bp22Q AeRJAJU4…zsb5tSEs

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.

3.882 × 10⁹⁵(96-digit number)

38820166828440672524…00089173783309305919

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

3.882 × 10⁹⁵(96-digit number)

38820166828440672524…00089173783309305919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.882 × 10⁹⁵(96-digit number)

38820166828440672524…00089173783309305921

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

7.764 × 10⁹⁵(96-digit number)

77640333656881345048…00178347566618611839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.764 × 10⁹⁵(96-digit number)

77640333656881345048…00178347566618611841

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

1.552 × 10⁹⁶(97-digit number)

15528066731376269009…00356695133237223679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.552 × 10⁹⁶(97-digit number)

15528066731376269009…00356695133237223681

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

3.105 × 10⁹⁶(97-digit number)

31056133462752538019…00713390266474447359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.105 × 10⁹⁶(97-digit number)

31056133462752538019…00713390266474447361

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

6.211 × 10⁹⁶(97-digit number)

62112266925505076038…01426780532948894719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.211 × 10⁹⁶(97-digit number)

62112266925505076038…01426780532948894721

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