Block #2,676,623

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/25/2018, 12:12:10 AM · Difficulty 11.6979 · 4,156,859 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

17dc0dc7800ede8a97e2b0163d253c76d9205eea8d0c6ac8b687a81a518a935f

View on Chainz ↗

Height

#2,676,623

Difficulty

11.697866

Transactions

Size

1.12 KB

Version

Bits

0bb2a760

Nonce

676,907,402

Timestamp

5/25/2018, 12:12:10 AM

Confirmations

4,156,859

Mined by

⛏️ P2SHAVpKSttrcp7W9V3CBDNWw3h2Q9Bj3kpRjG

Merkle Root

734cb6214b1ca37e2f3d64de175c54f5b6f86555611ea46368732a16352f0347

Transactions (4)

Coinbaseb49301ed5c6626…78fb51f5f8acba

1 in → 1 out7.3300 XPM109 B

AVpKSttr…Bj3kpRjG

0d7fe4ac261c7f…0b3f7b06c89f44

2 in → 2 out15.0900 XPM307 B

AUYGtJGo…44mbQ8s4 Af1EHpKc…FXFFFSou

94a5f53eb66d6c…94a74ea073a6f1

2 in → 2 out14.5900 XPM306 B

AYRSnuWj…VSqYH5PC AHZRKKFA…ELvY2MKQ

e6f255b7466642…ff78c6b2966640

2 in → 2 out11.0500 XPM339 B

AY9KEL9a…TL85ct5k AeB4qQo4…xQXaJErn

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.

3.542 × 10⁹⁵(96-digit number)

35426252864558837440…48450891882432511999

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

3.542 × 10⁹⁵(96-digit number)

35426252864558837440…48450891882432511999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.542 × 10⁹⁵(96-digit number)

35426252864558837440…48450891882432512001

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

7.085 × 10⁹⁵(96-digit number)

70852505729117674881…96901783764865023999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.085 × 10⁹⁵(96-digit number)

70852505729117674881…96901783764865024001

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

1.417 × 10⁹⁶(97-digit number)

14170501145823534976…93803567529730047999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.417 × 10⁹⁶(97-digit number)

14170501145823534976…93803567529730048001

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

2.834 × 10⁹⁶(97-digit number)

28341002291647069952…87607135059460095999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.834 × 10⁹⁶(97-digit number)

28341002291647069952…87607135059460096001

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

5.668 × 10⁹⁶(97-digit number)

56682004583294139905…75214270118920191999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.668 × 10⁹⁶(97-digit number)

56682004583294139905…75214270118920192001

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

1.133 × 10⁹⁷(98-digit number)

11336400916658827981…50428540237840383999

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 #2,676,623

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