Block #2,651,447

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/6/2018, 8:09:23 PM · Difficulty 11.7509 · 4,186,643 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

48308a17f702d2450dd960c937d0ec232a5eaf54ad327063c5f1099d48a01de8

View on Chainz ↗

Height

#2,651,447

Difficulty

11.750892

Transactions

Size

723 B

Version

Bits

0bc03a7c

Nonce

355,970,127

Timestamp

5/6/2018, 8:09:23 PM

Confirmations

4,186,643

Mined by

⛏️ P2SHAZy8vuwYzzqXHyVdn4UaF3bQmsRnKrVJfk

Merkle Root

5ee120239e626c46a2e9f2989823a80143c68349254ad70a34cd28eabe43853e

Transactions (2)

Coinbase82282f86d98910…a7bcbba9dad57d

1 in → 1 out7.2400 XPM110 B

AZy8vuwY…RnKrVJfk

12438242ee1eca…3aa85b562a632b

3 in → 2 out0.1274 XPM522 B

AYpwdL57…rVeBnBuy AKFaNWiE…vMCqi5Rq

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.

1.392 × 10⁹⁸(99-digit number)

13923857473951826974…16335619458576998399

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

1.392 × 10⁹⁸(99-digit number)

13923857473951826974…16335619458576998399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.392 × 10⁹⁸(99-digit number)

13923857473951826974…16335619458576998401

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

2.784 × 10⁹⁸(99-digit number)

27847714947903653949…32671238917153996799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.784 × 10⁹⁸(99-digit number)

27847714947903653949…32671238917153996801

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

5.569 × 10⁹⁸(99-digit number)

55695429895807307899…65342477834307993599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.569 × 10⁹⁸(99-digit number)

55695429895807307899…65342477834307993601

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

1.113 × 10⁹⁹(100-digit number)

11139085979161461579…30684955668615987199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.113 × 10⁹⁹(100-digit number)

11139085979161461579…30684955668615987201

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

2.227 × 10⁹⁹(100-digit number)

22278171958322923159…61369911337231974399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.227 × 10⁹⁹(100-digit number)

22278171958322923159…61369911337231974401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.455 × 10⁹⁹(100-digit number)

44556343916645846319…22739822674463948799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,651,447

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