Block #898,018

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/16/2015, 11:56:26 PM · Difficulty 10.9447 · 5,898,500 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2010f6464946fac3eb366da6b12ad0d7f633da36632b50e8f3aa6e75a1dea6c2

View on Chainz ↗

Height

#898,018

Difficulty

10.944726

Transactions

Size

1.15 KB

Version

Bits

0af1d995

Nonce

294,109,762

Timestamp

1/16/2015, 11:56:26 PM

Confirmations

5,898,500

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8eacb41066ad77bd06388dc98f6baf98afeef6873ede89e4a31283a3935c6d18

Transactions (4)

Coinbasebf385f365743b0…f1a4e1383072b7

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

e306903a98b271…1a2fd4da5b8639

1 in → 2 out5.2757 XPM226 B

AGCMTS6L…ekF5x9yz AMuYYsgd…ioD1TEUt

c97bb473bef909…6d349cc20deb68

1 in → 2 out4.7544 XPM226 B

ANbfkFwK…g5KSu7gC AHRoBSh4…BSVTQ36Q

2bcd29e5576a33…aecdb68f54d72b

3 in → 2 out5.2598 XPM520 B

AGDN4RqN…afGgHXGa ARpjHv1k…4F9NvuWN

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.

5.268 × 10⁹⁶(97-digit number)

52689086138636235144…37992584980150832639

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

5.268 × 10⁹⁶(97-digit number)

52689086138636235144…37992584980150832639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.268 × 10⁹⁶(97-digit number)

52689086138636235144…37992584980150832641

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

1.053 × 10⁹⁷(98-digit number)

10537817227727247028…75985169960301665279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.053 × 10⁹⁷(98-digit number)

10537817227727247028…75985169960301665281

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

2.107 × 10⁹⁷(98-digit number)

21075634455454494057…51970339920603330559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.107 × 10⁹⁷(98-digit number)

21075634455454494057…51970339920603330561

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

4.215 × 10⁹⁷(98-digit number)

42151268910908988115…03940679841206661119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.215 × 10⁹⁷(98-digit number)

42151268910908988115…03940679841206661121

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

8.430 × 10⁹⁷(98-digit number)

84302537821817976230…07881359682413322239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.430 × 10⁹⁷(98-digit number)

84302537821817976230…07881359682413322241

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

1.686 × 10⁹⁸(99-digit number)

16860507564363595246…15762719364826644479

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