Block #2,646,373

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2018, 8:10:15 AM · Difficulty 11.7490 · 4,186,845 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1fca3aa90b85b412cc664d2c31be9bcdfc807c4c5287a4d66017b44d545850e6

View on Chainz ↗

Height

#2,646,373

Difficulty

11.748977

Transactions

Size

1022 B

Version

Bits

0bbfbcf1

Nonce

801,453,133

Timestamp

5/3/2018, 8:10:15 AM

Confirmations

4,186,845

Mined by

⛏️ P2SHAJDzL3KKXoMKSDWjWkWeCNEZ7hvd4KuSSY

Merkle Root

b065bfd99f1eb8a73d7afcf2a067e34ba0d394f170c8cc5bf2baf25135c38ca8

Transactions (2)

Coinbaseff6996027464a5…d1275e4ddab969

1 in → 1 out7.2400 XPM110 B

AJDzL3KK…vd4KuSSY

32cfa74d68b801…3d184c237716b1

5 in → 2 out891.6628 XPM821 B

APdp7uLq…iPKaKpYx AXbkjKtU…bbu2XDF6

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.

3.986 × 10⁹⁶(97-digit number)

39869126122720532003…91355106826489036799

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

3.986 × 10⁹⁶(97-digit number)

39869126122720532003…91355106826489036799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.986 × 10⁹⁶(97-digit number)

39869126122720532003…91355106826489036801

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

7.973 × 10⁹⁶(97-digit number)

79738252245441064006…82710213652978073599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.973 × 10⁹⁶(97-digit number)

79738252245441064006…82710213652978073601

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

1.594 × 10⁹⁷(98-digit number)

15947650449088212801…65420427305956147199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.594 × 10⁹⁷(98-digit number)

15947650449088212801…65420427305956147201

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

3.189 × 10⁹⁷(98-digit number)

31895300898176425602…30840854611912294399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.189 × 10⁹⁷(98-digit number)

31895300898176425602…30840854611912294401

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

6.379 × 10⁹⁷(98-digit number)

63790601796352851205…61681709223824588799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.379 × 10⁹⁷(98-digit number)

63790601796352851205…61681709223824588801

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

1.275 × 10⁹⁸(99-digit number)

12758120359270570241…23363418447649177599

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 #2,646,373

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