Block #1,105,742

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/15/2015, 3:48:09 AM · Difficulty 10.7867 · 5,700,139 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2c1b3cc2a105063eacb2367bec5584cfe871e5f062fbde72cd6d0bcca4aba375

View on Chainz ↗

Height

#1,105,742

Difficulty

10.786726

Transactions

Size

3.31 KB

Version

Bits

0ac966da

Nonce

541,131,119

Timestamp

6/15/2015, 3:48:09 AM

Confirmations

5,700,139

Mined by

⛏️ P2SHAMTne5ighYXxjtjPRhwwnGNcsQiCWA4yhK

Merkle Root

38f982b24acf5d2353f97c8a5f0bf35db0fcd9f6a91a9803119cc1a24efffab9

Transactions (4)

Coinbase48726e86e0b77a…5d7f4228d97c61

1 in → 1 out8.7400 XPM109 B

AMTne5ig…iCWA4yhK

a7508a0e78dda2…c591dac0966b67

3 in → 2 out54440.0900 XPM521 B

ANtpa4Bw…HjzVT3bu ARyEuPxR…BVwXVJpR

d4bad35a76c352…259a51c752931a

1 in → 2 out14534.8231 XPM226 B

AV3Qzy8q…9nPoWiKv AH7bN5x2…af4NErwU

2d63f60f0f2152…c0756a44990267

16 in → 2 out555.4418 XPM2.39 KB

ANWSeHJc…ruR3SLaW AXBiJgtK…DteQDMxf

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.

5.900 × 10⁹⁶(97-digit number)

59003464543913384125…21793880458048245759

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

5.900 × 10⁹⁶(97-digit number)

59003464543913384125…21793880458048245759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.900 × 10⁹⁶(97-digit number)

59003464543913384125…21793880458048245761

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

1.180 × 10⁹⁷(98-digit number)

11800692908782676825…43587760916096491519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.180 × 10⁹⁷(98-digit number)

11800692908782676825…43587760916096491521

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

2.360 × 10⁹⁷(98-digit number)

23601385817565353650…87175521832192983039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.360 × 10⁹⁷(98-digit number)

23601385817565353650…87175521832192983041

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

4.720 × 10⁹⁷(98-digit number)

47202771635130707300…74351043664385966079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.720 × 10⁹⁷(98-digit number)

47202771635130707300…74351043664385966081

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

9.440 × 10⁹⁷(98-digit number)

94405543270261414601…48702087328771932159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.440 × 10⁹⁷(98-digit number)

94405543270261414601…48702087328771932161

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