Block #1,055,865

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/12/2015, 8:57:02 AM · Difficulty 10.7260 · 5,786,008 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a127e7e7a8c8a704d0d74bdedb74157dfd129a0154e621f3d56d496bdc0782a8

View on Chainz ↗

Height

#1,055,865

Difficulty

10.725968

Transactions

Size

50.08 KB

Version

Bits

0ab9d902

Nonce

1,005,931,611

Timestamp

5/12/2015, 8:57:02 AM

Confirmations

5,786,008

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

19fcc457dc14948f69142ee574d65a0fbad60268c28683bac7233d3dddf60920

Transactions (5)

Coinbase822c98ad28ccb1…e80e0e8540beff

1 in → 1 out9.2300 XPM116 B

ANSXnLY2…Sd25TjkD

28715f5f134677…8b412765740052

41 in → 2 out1165.0100 XPM6.00 KB

AR1BEChi…tvk57j6h AVgDhji8…PXWF9Z4F

59d3d009fcc22a…680890faf1f5d7

282 in → 2 out6646.6052 XPM40.84 KB

AeVFaBao…VrxTMC9j ATtzhtpj…onoidCoo

799fc12ad542c0…c3ccc7f096d128

6 in → 2 out29.9100 XPM965 B

Ad9anVQ2…CYp8PB3U AWMsnaGM…8LtnB8m9

00eb7b05d297e1…daa2b6110091a2

14 in → 2 out100.0496 XPM2.10 KB

AXhsX5xX…q2ccbLP5 AbddDA6d…Vxj8CuTA

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.

1.494 × 10⁹⁸(99-digit number)

14941793575182642121…21870261177170001919

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

1.494 × 10⁹⁸(99-digit number)

14941793575182642121…21870261177170001919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.494 × 10⁹⁸(99-digit number)

14941793575182642121…21870261177170001921

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

2.988 × 10⁹⁸(99-digit number)

29883587150365284242…43740522354340003839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.988 × 10⁹⁸(99-digit number)

29883587150365284242…43740522354340003841

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

5.976 × 10⁹⁸(99-digit number)

59767174300730568485…87481044708680007679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.976 × 10⁹⁸(99-digit number)

59767174300730568485…87481044708680007681

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

1.195 × 10⁹⁹(100-digit number)

11953434860146113697…74962089417360015359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.195 × 10⁹⁹(100-digit number)

11953434860146113697…74962089417360015361

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

2.390 × 10⁹⁹(100-digit number)

23906869720292227394…49924178834720030719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.390 × 10⁹⁹(100-digit number)

23906869720292227394…49924178834720030721

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 #1,055,865

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