Block #2,616,268

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/16/2018, 8:57:53 AM · Difficulty 11.2254 · 4,189,093 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9f8e7eebfaf59333234a96a4852cdb6873a791c43e54c5bb97564e85f911fbea

View on Chainz ↗

Height

#2,616,268

Difficulty

11.225382

Transactions

Size

94.36 KB

Version

Bits

0b39b2a7

Nonce

290,949,713

Timestamp

4/16/2018, 8:57:53 AM

Confirmations

4,189,093

Mined by

⛏️ P2SHAaKtjZgvtLUL2s3QsCZyK3iW1vuDEZeNvU

Merkle Root

0cf644f5dffc41c5b91792ca280401a9c140cef3480fe813b5487bcc84dfdb34

Transactions (5)

Coinbase158a848243091c…06f1a27d234c53

1 in → 1 out8.9100 XPM110 B

AaKtjZgv…uDEZeNvU

8a1aafab71021f…aec14b971a3149

641 in → 2 out700.0100 XPM92.73 KB

AN3qzDd9…iLm7bcZK ALPF8J52…Hjw4BMsG

84293b2b34644e…02e8c227663a97

2 in → 2 out15.8800 XPM307 B

AS1WSsdu…SsSskEP2 ALYwKGdq…iUeLR8sm

f1d16772ae9a0f…f8c02a147c11fb

2 in → 2 out11.7600 XPM341 B

AWgUh2j1…5TjboMjv AM6XD26m…RcphfPC1

b389aa7835272f…c44b48e622b3b5

5 in → 2 out120.4829 XPM819 B

ATGkMJ3M…LQkhTAXw AawcLscQ…16WKsAb5

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.

9.213 × 10⁹⁴(95-digit number)

92133944748564996036…20466645550702079999

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

9.213 × 10⁹⁴(95-digit number)

92133944748564996036…20466645550702079999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.213 × 10⁹⁴(95-digit number)

92133944748564996036…20466645550702080001

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

1.842 × 10⁹⁵(96-digit number)

18426788949712999207…40933291101404159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.842 × 10⁹⁵(96-digit number)

18426788949712999207…40933291101404160001

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

3.685 × 10⁹⁵(96-digit number)

36853577899425998414…81866582202808319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.685 × 10⁹⁵(96-digit number)

36853577899425998414…81866582202808320001

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

7.370 × 10⁹⁵(96-digit number)

73707155798851996828…63733164405616639999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.370 × 10⁹⁵(96-digit number)

73707155798851996828…63733164405616640001

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

1.474 × 10⁹⁶(97-digit number)

14741431159770399365…27466328811233279999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.474 × 10⁹⁶(97-digit number)

14741431159770399365…27466328811233280001

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

2.948 × 10⁹⁶(97-digit number)

29482862319540798731…54932657622466559999

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