Block #347,067

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/6/2014, 10:44:45 PM · Difficulty 10.2379 · 6,449,492 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4623aa9d90a9b8894420ff9fc7c8962082c5477eaf6baa3390ab4f9ac80af72f

View on Chainz ↗

Height

#347,067

Difficulty

10.237871

Transactions

Size

1.08 KB

Version

Bits

0a3ce51c

Nonce

3,172

Timestamp

1/6/2014, 10:44:45 PM

Confirmations

6,449,492

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

6507b700917d24bd6e4a32f1956b6c597facca98df97c1592ccbab1f90a5bb81

Transactions (5)

Coinbasef2896002e882a9…eddf240adaf6a3

1 in → 1 out9.5700 XPM110 B

AeKNrjNj…1NEq95Ta

adc3db7c80b157…38b7c2cd6ef61a

1 in → 2 out8.5943 XPM227 B

AHLSSm7i…KoJQXcah AecyRELh…qvzL83oe

04a7334d2f207f…7ec8a661280f40

1 in → 2 out6.5726 XPM226 B

AQAph9Ee…Bh4omZLF AYxsEPCY…QQvyetDE

69809ca3579797…56b3614d7f76cb

1 in → 2 out4.5290 XPM226 B

AMNCsDeK…6ZBsricT Acw2CKaE…BEkjuKFo

25b3fe91749a8a…f5efee191201d2

1 in → 2 out2.0901 XPM227 B

AHFGR79p…9mXDf11Y AUq1WLGN…F4abwcBR

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.

2.986 × 10⁹⁵(96-digit number)

29866586490339028362…96196394841291438079

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

2.986 × 10⁹⁵(96-digit number)

29866586490339028362…96196394841291438079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.986 × 10⁹⁵(96-digit number)

29866586490339028362…96196394841291438081

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

5.973 × 10⁹⁵(96-digit number)

59733172980678056724…92392789682582876159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.973 × 10⁹⁵(96-digit number)

59733172980678056724…92392789682582876161

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

1.194 × 10⁹⁶(97-digit number)

11946634596135611344…84785579365165752319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.194 × 10⁹⁶(97-digit number)

11946634596135611344…84785579365165752321

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

2.389 × 10⁹⁶(97-digit number)

23893269192271222689…69571158730331504639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.389 × 10⁹⁶(97-digit number)

23893269192271222689…69571158730331504641

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

4.778 × 10⁹⁶(97-digit number)

47786538384542445379…39142317460663009279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.778 × 10⁹⁶(97-digit number)

47786538384542445379…39142317460663009281

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