Block #903,664

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/21/2015, 7:56:06 AM · Difficulty 10.9381 · 5,906,750 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ea43d36388423d212de26ed0f76b63db4b35d350729bd760a39816eddaabefb0

View on Chainz ↗

Height

#903,664

Difficulty

10.938051

Transactions

Size

7.50 KB

Version

Bits

0af02420

Nonce

325,322,564

Timestamp

1/21/2015, 7:56:06 AM

Confirmations

5,906,750

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

dd390f4aaa0460f5c18a4ba4d843227dc43d959380e1605b0f3fa07f67b3d495

Transactions (2)

Coinbase3aea8519327a60…daed70653ee26b

1 in → 1 out8.4200 XPM116 B

ANSXnLY2…Sd25TjkD

c88ae41a5bae05…bd1bf8c04fed38

50 in → 2 out7870.1645 XPM7.29 KB

ARz892XW…t8odcy26 AXpqdsNv…NLKNZsGB

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.

6.221 × 10⁹⁹(100-digit number)

62217612769630036792…00491171072966655999

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

6.221 × 10⁹⁹(100-digit number)

62217612769630036792…00491171072966655999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.221 × 10⁹⁹(100-digit number)

62217612769630036792…00491171072966656001

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

1.244 × 10¹⁰⁰(101-digit number)

12443522553926007358…00982342145933311999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.244 × 10¹⁰⁰(101-digit number)

12443522553926007358…00982342145933312001

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

2.488 × 10¹⁰⁰(101-digit number)

24887045107852014717…01964684291866623999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.488 × 10¹⁰⁰(101-digit number)

24887045107852014717…01964684291866624001

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

4.977 × 10¹⁰⁰(101-digit number)

49774090215704029434…03929368583733247999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.977 × 10¹⁰⁰(101-digit number)

49774090215704029434…03929368583733248001

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

9.954 × 10¹⁰⁰(101-digit number)

99548180431408058868…07858737167466495999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.954 × 10¹⁰⁰(101-digit number)

99548180431408058868…07858737167466496001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #903,664

Cookie Preferences