Block #1,049,364

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/7/2015, 8:13:23 PM · Difficulty 10.7270 · 5,757,090 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ea69093ac686b5eed8269c7b09d0772a1ab13097e278088912ec1e40420565ae

View on Chainz ↗

Height

#1,049,364

Difficulty

10.726974

Transactions

Size

3.90 KB

Version

Bits

0aba1af4

Nonce

2,116,825,936

Timestamp

5/7/2015, 8:13:23 PM

Confirmations

5,757,090

Mined by

⛏️ 5ANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8b541ce594d986aa178eac8e98299690d9a08b63abb0a1bf0d0014191e1912fc

Transactions (3)

Coinbasee75dd5004ffeda…78b713c39e88d6

1 in → 1 out8.7200 XPM116 B

ANSXnLY2…Sd25TjkD

10ca017b63969e…27778af7253448

1 in → 51 out34.2843 XPM1.85 KB

AHKGrFmR…qVzPRPxj ASG21nzq…iMYaGLq3 AHjwfhMe…6kjquBob AG7DRd78…Lhvirwcu AHbDM4BA…Q1CRsUDy

a74fb03bdd4a41…bd8a801ba59120

1 in → 51 out11.0994 XPM1.85 KB

AbkgeLEA…iFNYa3vD AHiVFmS7…SSWQafCc AeGBT27q…KsPD3Z37 APM3RoGj…Vb6frVuB ANyTQbRi…ei3sdhN1

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.

8.997 × 10⁹⁸(99-digit number)

89973779355782421181…54730751032711741439

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

8.997 × 10⁹⁸(99-digit number)

89973779355782421181…54730751032711741439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.997 × 10⁹⁸(99-digit number)

89973779355782421181…54730751032711741441

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

1.799 × 10⁹⁹(100-digit number)

17994755871156484236…09461502065423482879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.799 × 10⁹⁹(100-digit number)

17994755871156484236…09461502065423482881

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

3.598 × 10⁹⁹(100-digit number)

35989511742312968472…18923004130846965759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.598 × 10⁹⁹(100-digit number)

35989511742312968472…18923004130846965761

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

7.197 × 10⁹⁹(100-digit number)

71979023484625936945…37846008261693931519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.197 × 10⁹⁹(100-digit number)

71979023484625936945…37846008261693931521

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

1.439 × 10¹⁰⁰(101-digit number)

14395804696925187389…75692016523387863039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.439 × 10¹⁰⁰(101-digit number)

14395804696925187389…75692016523387863041

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

2.879 × 10¹⁰⁰(101-digit number)

28791609393850374778…51384033046775726079

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 #1,049,364

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