Block #1,278,905

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/12/2015, 4:51:16 PM · Difficulty 10.8344 · 5,531,642 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c4128d222b445f1df10bbade1e12d77af3c4b02247e0c24102389dc456cf1902

View on Chainz ↗

Height

#1,278,905

Difficulty

10.834407

Transactions

Size

652 B

Version

Bits

0ad59bb2

Nonce

503,162,624

Timestamp

10/12/2015, 4:51:16 PM

Confirmations

5,531,642

Mined by

⛏️ P2SHAYJJhrGTWenVxqqVue1u36dMfEL6VffxTu

Merkle Root

f624635150b90540f898d0617003dfbf91abc231fceeb2ee1187d98ce4e59412

Transactions (3)

Coinbasee8201b2475c022…bda502693fe784

1 in → 1 out8.5300 XPM109 B

AYJJhrGT…L6VffxTu

d027c4bb960c99…a514b5f6e11918

1 in → 2 out7.4793 XPM226 B

AJ6VjfsP…ZapauyVV ANfwhsyh…iYEHnbDU

e4fa48154a1956…afd7e7685777ec

1 in → 2 out3.8652 XPM226 B

AWTLSMsP…RKipi4Px AXrTw46X…e1dGvSFf

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.

1.081 × 10⁹⁸(99-digit number)

10818143860762096165…31579637336784240639

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

1.081 × 10⁹⁸(99-digit number)

10818143860762096165…31579637336784240639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.081 × 10⁹⁸(99-digit number)

10818143860762096165…31579637336784240641

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

2.163 × 10⁹⁸(99-digit number)

21636287721524192331…63159274673568481279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.163 × 10⁹⁸(99-digit number)

21636287721524192331…63159274673568481281

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

4.327 × 10⁹⁸(99-digit number)

43272575443048384662…26318549347136962559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.327 × 10⁹⁸(99-digit number)

43272575443048384662…26318549347136962561

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

8.654 × 10⁹⁸(99-digit number)

86545150886096769325…52637098694273925119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.654 × 10⁹⁸(99-digit number)

86545150886096769325…52637098694273925121

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

1.730 × 10⁹⁹(100-digit number)

17309030177219353865…05274197388547850239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.730 × 10⁹⁹(100-digit number)

17309030177219353865…05274197388547850241

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 #1,278,905

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