Block #2,095,310

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/1/2017, 5:00:14 AM · Difficulty 10.8725 · 4,731,485 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bb52e37658b7b30d2ad0c5743f6ec6ec502e0ba3fea6e36360184a5abea018e6

View on Chainz ↗

Height

#2,095,310

Difficulty

10.872513

Transactions

Size

3.07 KB

Version

Bits

0adf5d04

Nonce

273,824,018

Timestamp

5/1/2017, 5:00:14 AM

Confirmations

4,731,485

Mined by

⛏️ P2SHAQo1VWZtGm3hJrPhGzZGXDPC2nokoMvx2d

Merkle Root

655762333aa165875514aebc724b2774af3e8543de2d265f66661e650b87619f

Transactions (4)

Coinbasebf78dec68bf828…515c65d8dcf843

1 in → 1 out8.4900 XPM109 B

AQo1VWZt…okoMvx2d

756cdbcd8a13e8…1f47536e95866f

12 in → 2 out839.1743 XPM1.80 KB

AYkGC9iw…uGtwsctN AcXSJmYj…1UQKGSCx

74186be1ce4554…26d6fc00da3d95

7 in → 2 out59.1300 XPM875 B

AJ8zygws…xxzNnTmn AMLiyYLv…iYQLf2JU

2a2cc2553bd79e…e896f5c23f8212

1 in → 2 out3.1892 XPM226 B

AKtpRgwP…6SgEFUJ3 AeYZTP6b…v53Q54vJ

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.

4.632 × 10⁹⁷(98-digit number)

46323825612029591191…91863489063355351039

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

4.632 × 10⁹⁷(98-digit number)

46323825612029591191…91863489063355351039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.632 × 10⁹⁷(98-digit number)

46323825612029591191…91863489063355351041

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

9.264 × 10⁹⁷(98-digit number)

92647651224059182382…83726978126710702079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.264 × 10⁹⁷(98-digit number)

92647651224059182382…83726978126710702081

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

1.852 × 10⁹⁸(99-digit number)

18529530244811836476…67453956253421404159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.852 × 10⁹⁸(99-digit number)

18529530244811836476…67453956253421404161

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

3.705 × 10⁹⁸(99-digit number)

37059060489623672953…34907912506842808319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.705 × 10⁹⁸(99-digit number)

37059060489623672953…34907912506842808321

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

7.411 × 10⁹⁸(99-digit number)

74118120979247345906…69815825013685616639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.411 × 10⁹⁸(99-digit number)

74118120979247345906…69815825013685616641

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 #2,095,310

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