Block #345,014

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/5/2014, 3:42:26 PM · Difficulty 10.2079 · 6,446,699 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1945af40124d6fb8008e728667581ea2d0a4effa94caa08b2dcab6038d6bb242

View on Chainz ↗

Height

#345,014

Difficulty

10.207889

Transactions

Size

1.19 KB

Version

Bits

0a35383c

Nonce

3,958

Timestamp

1/5/2014, 3:42:26 PM

Confirmations

6,446,699

Merkle Root

8bea726539e8df9a17e944a99c6595113510897c08f56ad7e8180fcf88ad2d58

Transactions (5)

Coinbase5ddf2ada3b9652…bc5bbb5d084e28

1 in → 1 out9.6200 XPM109 B

AGssgv8C…zT3wunSb

dd18a672c8784e…461382ed2edb7b

2 in → 2 out99.9100 XPM375 B

AK9Drama…rB1fKBN4 AWMhP23A…UK7yorCx

8bf06f6638d4f6…99667af497fe37

1 in → 1 out0.2946 XPM192 B

ALvb4UXn…UdswbBD5

598a54b0b92435…45bd5403bb762a

1 in → 2 out888.8498 XPM226 B

Aerr6ngM…ohk6P8QT AVikjSro…vsDnpzS1

c9766d7106a507…5125152f64b4d0

1 in → 2 out7.6795 XPM227 B

AMpM6zp5…GgoVEJx5 AeKdMwbk…Zuuysysf

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.

2.287 × 10⁹⁷(98-digit number)

22878561476934514589…59486086766974282879

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

2.287 × 10⁹⁷(98-digit number)

22878561476934514589…59486086766974282879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.287 × 10⁹⁷(98-digit number)

22878561476934514589…59486086766974282881

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

4.575 × 10⁹⁷(98-digit number)

45757122953869029178…18972173533948565759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.575 × 10⁹⁷(98-digit number)

45757122953869029178…18972173533948565761

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

9.151 × 10⁹⁷(98-digit number)

91514245907738058356…37944347067897131519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.151 × 10⁹⁷(98-digit number)

91514245907738058356…37944347067897131521

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

1.830 × 10⁹⁸(99-digit number)

18302849181547611671…75888694135794263039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.830 × 10⁹⁸(99-digit number)

18302849181547611671…75888694135794263041

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

3.660 × 10⁹⁸(99-digit number)

36605698363095223342…51777388271588526079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.660 × 10⁹⁸(99-digit number)

36605698363095223342…51777388271588526081

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