Block #349,987

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/8/2014, 5:53:32 PM · Difficulty 10.2869 · 6,444,365 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

05ec8cd1937a5b8f98a24ca34a5d645606adf55144d953fbe3fd0da56db12632

View on Chainz ↗

Height

#349,987

Difficulty

10.286869

Transactions

Size

392 B

Version

Bits

0a497042

Nonce

170,092

Timestamp

1/8/2014, 5:53:32 PM

Confirmations

6,444,365

Merkle Root

35f58a002fdf2e8a045a05e7f6bd66a620e45968d5da4c88edfa8494a7b0ad3a

Transactions (2)

Coinbase1c0881c6a1f81c…80d4615fd600b7

1 in → 1 out9.4500 XPM110 B

AeKNrjNj…1NEq95Ta

2f435c3c91d2a0…71928d93eababa

1 in → 1 out3.1726 XPM193 B

AQ7CPjhw…fxeUh3L8

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.

1.691 × 10⁹³(94-digit number)

16912604111984251478…12633320311136089739

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

1.691 × 10⁹³(94-digit number)

16912604111984251478…12633320311136089739

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.691 × 10⁹³(94-digit number)

16912604111984251478…12633320311136089741

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

3.382 × 10⁹³(94-digit number)

33825208223968502957…25266640622272179479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.382 × 10⁹³(94-digit number)

33825208223968502957…25266640622272179481

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

6.765 × 10⁹³(94-digit number)

67650416447937005914…50533281244544358959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.765 × 10⁹³(94-digit number)

67650416447937005914…50533281244544358961

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

1.353 × 10⁹⁴(95-digit number)

13530083289587401182…01066562489088717919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.353 × 10⁹⁴(95-digit number)

13530083289587401182…01066562489088717921

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

2.706 × 10⁹⁴(95-digit number)

27060166579174802365…02133124978177435839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.706 × 10⁹⁴(95-digit number)

27060166579174802365…02133124978177435841

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