Block #419,118

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/25/2014, 9:16:24 AM · Difficulty 10.3851 · 6,386,985 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0f688d8d58d6aa02699dc7d6d845395a0c1367a87219a86a3079088bfcfe2ee6

View on Chainz ↗

Height

#419,118

Difficulty

10.385109

Transactions

Size

684 B

Version

Bits

0a629680

Nonce

8,422

Timestamp

2/25/2014, 9:16:24 AM

Confirmations

6,386,985

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

3ed66d0b442261d8fff7217a26ba68b41174aba356bafe749b095d3793d2a190

Transactions (2)

Coinbase2f9d23498e099a…a5a86fa6b8b14d

1 in → 1 out9.2700 XPM116 B

AbwWkWZt…kawDhufa

cd326e03ed9e1b…62b50481b0d166

2 in → 7 out18.4500 XPM475 B

ARK3p4G1…7Pe4FNSw AeKNrjNj…1NEq95Ta AW7MfWAo…caab44fx AbfkiWwg…fhe7yhRU AJqSCMbE…ELzwpPmc

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.

4.077 × 10¹⁰¹(102-digit number)

40776827717583212243…67860303898131103999

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

4.077 × 10¹⁰¹(102-digit number)

40776827717583212243…67860303898131103999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.077 × 10¹⁰¹(102-digit number)

40776827717583212243…67860303898131104001

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

8.155 × 10¹⁰¹(102-digit number)

81553655435166424487…35720607796262207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.155 × 10¹⁰¹(102-digit number)

81553655435166424487…35720607796262208001

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

1.631 × 10¹⁰²(103-digit number)

16310731087033284897…71441215592524415999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.631 × 10¹⁰²(103-digit number)

16310731087033284897…71441215592524416001

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

3.262 × 10¹⁰²(103-digit number)

32621462174066569795…42882431185048831999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.262 × 10¹⁰²(103-digit number)

32621462174066569795…42882431185048832001

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

6.524 × 10¹⁰²(103-digit number)

65242924348133139590…85764862370097663999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.524 × 10¹⁰²(103-digit number)

65242924348133139590…85764862370097664001

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