Block #279,416

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 8:25:50 AM · Difficulty 9.9717 · 6,526,974 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

81382b8da71900f0de8d7b893221910a1b6f051bb1921d44e100844266331058

View on Chainz ↗

Height

#279,416

Difficulty

9.971676

Transactions

Size

3.47 KB

Version

Bits

09f8bfc5

Nonce

158,365

Timestamp

11/28/2013, 8:25:50 AM

Confirmations

6,526,974

Mined by

⛏️ xCaR"AbtgNzNbw1hJh3uoaBwXxdpmiY9Atvu81w

Merkle Root

82e2b2bba3aa854a9c59feda8a954a2c4f4fffbbf0540ae8ff1329685a001aa8

Transactions (4)

Coinbase6a3bb9a7bc56c0…3b97203c1c4ea2

1 in → 29 out10.0200 XPM1.02 KB

AbtgNzNb…9Atvu81w AScAzqGc…BZ6tV1vJ AN8nUzff…YcDfRDQ2 AQyr8Lw3…hs4nt3Pn ALw8WzMm…sj2uYfgL

77beecaf8a6fd4…3e51d97aaaca6e

13 in → 1 out7.1796 XPM1.92 KB

ANE24o82…isqEEY2z

649a5b3711ac5a…339c902b10a6f5

1 in → 2 out9.0267 XPM225 B

AZtFPifF…DaugVair ATrfosjk…hhBj3euX

c2ba5f1f477bb6…1d941d79d70411

1 in → 2 out9.0200 XPM226 B

ARJruFoN…R4cPNMsf AKSCbyGd…RZXiPFhz

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.

7.216 × 10⁹¹(92-digit number)

72169877165249707468…84722864847299185479

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

7.216 × 10⁹¹(92-digit number)

72169877165249707468…84722864847299185479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.216 × 10⁹¹(92-digit number)

72169877165249707468…84722864847299185481

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

1.443 × 10⁹²(93-digit number)

14433975433049941493…69445729694598370959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.443 × 10⁹²(93-digit number)

14433975433049941493…69445729694598370961

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

2.886 × 10⁹²(93-digit number)

28867950866099882987…38891459389196741919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.886 × 10⁹²(93-digit number)

28867950866099882987…38891459389196741921

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

5.773 × 10⁹²(93-digit number)

57735901732199765974…77782918778393483839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.773 × 10⁹²(93-digit number)

57735901732199765974…77782918778393483841

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

1.154 × 10⁹³(94-digit number)

11547180346439953194…55565837556786967679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.154 × 10⁹³(94-digit number)

11547180346439953194…55565837556786967681

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 #279,416

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