Block #2,190,981

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/3/2017, 11:18:13 AM · Difficulty 10.9502 · 4,642,291 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d1b0eec092050ff24689a653bf0a8e0d701c117cc817764a4a4439f7735f6fbd

View on Chainz ↗

Height

#2,190,981

Difficulty

10.950190

Transactions

Size

1.21 KB

Version

Bits

0af33fa5

Nonce

1,508,320,465

Timestamp

7/3/2017, 11:18:13 AM

Confirmations

4,642,291

Mined by

⛏️ P2SHAZoyp6gwHXNLUDMCBE5GPaNZfKYwyppWfg

Merkle Root

5d15fcfc21d60f0426f7704602a420204231177f731e15925395e50b8a065ed2

Transactions (3)

Coinbase2cedd1e180bf4c…0b4d4224b2821d

1 in → 1 out8.3600 XPM110 B

AZoyp6gw…YwyppWfg

ee04bcfeab2597…406aff1fbda1e5

3 in → 2 out1209.5568 XPM522 B

AdzcYqGi…3nWuJHoa Ac5nA7GH…26NRN9FN

02933b25c1e371…2f84ea84be6186

3 in → 2 out511.3494 XPM521 B

AYVBmLey…e5tVN1ar ANHVfWfb…VWLVJ3z3

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.

1.376 × 10⁹⁶(97-digit number)

13761872291977325674…84109914314879482879

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

1.376 × 10⁹⁶(97-digit number)

13761872291977325674…84109914314879482879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.376 × 10⁹⁶(97-digit number)

13761872291977325674…84109914314879482881

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

2.752 × 10⁹⁶(97-digit number)

27523744583954651348…68219828629758965759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.752 × 10⁹⁶(97-digit number)

27523744583954651348…68219828629758965761

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

5.504 × 10⁹⁶(97-digit number)

55047489167909302697…36439657259517931519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.504 × 10⁹⁶(97-digit number)

55047489167909302697…36439657259517931521

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

1.100 × 10⁹⁷(98-digit number)

11009497833581860539…72879314519035863039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.100 × 10⁹⁷(98-digit number)

11009497833581860539…72879314519035863041

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

2.201 × 10⁹⁷(98-digit number)

22018995667163721078…45758629038071726079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.201 × 10⁹⁷(98-digit number)

22018995667163721078…45758629038071726081

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

4.403 × 10⁹⁷(98-digit number)

44037991334327442157…91517258076143452159

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 #2,190,981

Cookie Preferences