Block #1,115,120

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/18/2015, 7:27:18 AM · Difficulty 10.9185 · 5,700,816 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b9a3920fcc15a59c73c82c58f8bcf7b9029c73e5dacdcb03334238e73c21d3df

View on Chainz ↗

Height

#1,115,120

Difficulty

10.918476

Transactions

Size

1.07 KB

Version

Bits

0aeb2143

Nonce

271,951,349

Timestamp

6/18/2015, 7:27:18 AM

Confirmations

5,700,816

Mined by

⛏️ P2SHAZRNkHboyMquNgMnQgmbvrVkKLLzpoRvQ4

Merkle Root

e103fd19966c019c00d45bac7aa5e77a7498c7ac071fa42d0efacb67ff398fc9

Transactions (3)

Coinbase36cbb57777c13c…22bcf8e0e1403b

1 in → 1 out8.3900 XPM110 B

AZRNkHbo…LzpoRvQ4

9d4a71ccdbcc2b…d37328e096025b

4 in → 2 out989.0207 XPM669 B

AMi4LCwa…xB6SYcCA AV9s3vDX…YPoAWs3Q

305d70ddfc03b6…b22b0c31d826fc

1 in → 2 out5.7082 XPM225 B

Aa8zovdV…ntNb2fui AdqWXbiB…GTi1p6x9

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.

4.853 × 10⁹⁴(95-digit number)

48532727747282851360…37985900771526676479

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

4.853 × 10⁹⁴(95-digit number)

48532727747282851360…37985900771526676479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.853 × 10⁹⁴(95-digit number)

48532727747282851360…37985900771526676481

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

9.706 × 10⁹⁴(95-digit number)

97065455494565702721…75971801543053352959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.706 × 10⁹⁴(95-digit number)

97065455494565702721…75971801543053352961

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

1.941 × 10⁹⁵(96-digit number)

19413091098913140544…51943603086106705919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.941 × 10⁹⁵(96-digit number)

19413091098913140544…51943603086106705921

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

3.882 × 10⁹⁵(96-digit number)

38826182197826281088…03887206172213411839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.882 × 10⁹⁵(96-digit number)

38826182197826281088…03887206172213411841

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

7.765 × 10⁹⁵(96-digit number)

77652364395652562177…07774412344426823679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.765 × 10⁹⁵(96-digit number)

77652364395652562177…07774412344426823681

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

Block #1,115,120

Cookie Preferences