Block #1,055,190

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/11/2015, 9:44:08 PM · Difficulty 10.7258 · 5,755,911 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3bec85abe3480900839f7e94ed7f767d26e99ceac876c712a26cf3df66d9f2da

View on Chainz ↗

Height

#1,055,190

Difficulty

10.725837

Transactions

Size

3.15 KB

Version

Bits

0ab9d07a

Nonce

172,421,635

Timestamp

5/11/2015, 9:44:08 PM

Confirmations

5,755,911

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f119d65b601e59fcd1e76ebd60e9ede2b9d41f2fdc9dc5b28cd173417668a9ac

Transactions (5)

Coinbase8adf81bb07730f…36b05df9cbe74f

1 in → 1 out8.7300 XPM116 B

ANSXnLY2…Sd25TjkD

bcd552f69a91e6…496451f1d3344e

1 in → 2 out8.6400 XPM226 B

ATfSTCKJ…PhdtdHSq AYccseR6…53LPVtb8

1d92d1154133c1…d7374697307d24

4 in → 2 out16.0236 XPM670 B

AVDsiKfN…DcYfcokt AeZY3cgZ…91rSeNie

7465bac3b58cdd…8d3e0617e77ae0

1 in → 51 out15.3591 XPM1.85 KB

AbkgeLEA…iFNYa3vD AYwBymsD…itUaTwWu AL7pfBqe…e4Z6fLbe AZGfyPT7…D6Q1Rc6D ASpHaAd8…jFLe2Byo

019d837db6ecc2…af860517fcf360

1 in → 2 out7.5694 XPM227 B

AVWS2z5m…ENPF1ZyC ATNigJi1…EH6t1JCN

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.

1.503 × 10⁹⁵(96-digit number)

15039489809768212463…36254939682516239359

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

1.503 × 10⁹⁵(96-digit number)

15039489809768212463…36254939682516239359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.503 × 10⁹⁵(96-digit number)

15039489809768212463…36254939682516239361

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

3.007 × 10⁹⁵(96-digit number)

30078979619536424926…72509879365032478719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.007 × 10⁹⁵(96-digit number)

30078979619536424926…72509879365032478721

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

6.015 × 10⁹⁵(96-digit number)

60157959239072849852…45019758730064957439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.015 × 10⁹⁵(96-digit number)

60157959239072849852…45019758730064957441

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

1.203 × 10⁹⁶(97-digit number)

12031591847814569970…90039517460129914879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.203 × 10⁹⁶(97-digit number)

12031591847814569970…90039517460129914881

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

2.406 × 10⁹⁶(97-digit number)

24063183695629139941…80079034920259829759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.406 × 10⁹⁶(97-digit number)

24063183695629139941…80079034920259829761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.812 × 10⁹⁶(97-digit number)

48126367391258279882…60158069840519659519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,055,190

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