Block #2,664,245

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/16/2018, 9:36:01 PM · Difficulty 11.6525 · 4,175,431 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a902e2345b8b69ec2ed2fee9001f2a0dfd5b87d9fd01a8094b60f3838250c27d

View on Chainz ↗

Height

#2,664,245

Difficulty

11.652490

Transactions

Size

722 B

Version

Bits

0ba70992

Nonce

849,682,188

Timestamp

5/16/2018, 9:36:01 PM

Confirmations

4,175,431

Mined by

⛏️ P2SHAVSfHErn3fVRYnhj4y7Mp1N6rQ9eTWwL3s

Merkle Root

26897c174e29c464f1ad2cc9ad1bcea3786c783e3d19718117b702ab94ce4e72

Transactions (2)

Coinbase91f89933b9aa32…99d001094f494c

1 in → 1 out7.3600 XPM110 B

AVSfHErn…9eTWwL3s

598de23ee85861…a75f8ea38781c7

3 in → 2 out4500.0102 XPM521 B

AH3A2GJU…NLYdkucb AGDw7M5Z…kiakhBXN

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.

8.642 × 10⁹⁶(97-digit number)

86428306389222594777…43308994895407662079

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

8.642 × 10⁹⁶(97-digit number)

86428306389222594777…43308994895407662079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.642 × 10⁹⁶(97-digit number)

86428306389222594777…43308994895407662081

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

1.728 × 10⁹⁷(98-digit number)

17285661277844518955…86617989790815324159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.728 × 10⁹⁷(98-digit number)

17285661277844518955…86617989790815324161

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

3.457 × 10⁹⁷(98-digit number)

34571322555689037910…73235979581630648319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.457 × 10⁹⁷(98-digit number)

34571322555689037910…73235979581630648321

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

6.914 × 10⁹⁷(98-digit number)

69142645111378075821…46471959163261296639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.914 × 10⁹⁷(98-digit number)

69142645111378075821…46471959163261296641

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

1.382 × 10⁹⁸(99-digit number)

13828529022275615164…92943918326522593279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.382 × 10⁹⁸(99-digit number)

13828529022275615164…92943918326522593281

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

2.765 × 10⁹⁸(99-digit number)

27657058044551230328…85887836653045186559

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 #2,664,245

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