Block #902,340

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2015, 6:48:41 AM · Difficulty 10.9402 · 5,892,175 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

45f63effbaa3187d5af77bd37ce7f62f15211742fcb8dee646952ec55cafa858

View on Chainz ↗

Height

#902,340

Difficulty

10.940187

Transactions

Size

13.86 KB

Version

Bits

0af0b018

Nonce

676,083,974

Timestamp

1/20/2015, 6:48:41 AM

Confirmations

5,892,175

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

71e04c09ed0ab830262a9217da43bdde4970ee845267aa03746e434c20cc9e4a

Transactions (2)

Coinbase0f06a46e37538d…6f655c3583f3e5

1 in → 1 out8.4900 XPM116 B

ANSXnLY2…Sd25TjkD

33ee42f192411b…cc1b01b3b7ff8f

94 in → 2 out69999.9100 XPM13.66 KB

AZMhKjWv…JhxLguFA ATYgCRTJ…kWCnPgm5

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.

1.624 × 10⁹⁶(97-digit number)

16240521566224741257…97975579605181027999

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

1.624 × 10⁹⁶(97-digit number)

16240521566224741257…97975579605181027999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.624 × 10⁹⁶(97-digit number)

16240521566224741257…97975579605181028001

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

3.248 × 10⁹⁶(97-digit number)

32481043132449482514…95951159210362055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.248 × 10⁹⁶(97-digit number)

32481043132449482514…95951159210362056001

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

6.496 × 10⁹⁶(97-digit number)

64962086264898965029…91902318420724111999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.496 × 10⁹⁶(97-digit number)

64962086264898965029…91902318420724112001

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

1.299 × 10⁹⁷(98-digit number)

12992417252979793005…83804636841448223999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.299 × 10⁹⁷(98-digit number)

12992417252979793005…83804636841448224001

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

2.598 × 10⁹⁷(98-digit number)

25984834505959586011…67609273682896447999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.598 × 10⁹⁷(98-digit number)

25984834505959586011…67609273682896448001

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