Block #2,739,736

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/8/2018, 3:56:47 PM · Difficulty 11.6199 · 4,100,025 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8505ab7c81216305fb298d8dd772a7330363b444788edbd87575dde343c52089

View on Chainz ↗

Height

#2,739,736

Difficulty

11.619912

Transactions

Size

768 B

Version

Bits

0b9eb28b

Nonce

2,060,307,404

Timestamp

7/8/2018, 3:56:47 PM

Confirmations

4,100,025

Mined by

⛏️ P2SHAUyqspftEjaXdXR5GjH5LVzPRs5WF2WW3f

Merkle Root

bcd310108785ca6a1b17c363eded351776d0d8eb186deeaa3d7ef3e9637d6613

Transactions (3)

Coinbase812c47ba748e40…7bb7500f3e9beb

1 in → 1 out7.4100 XPM110 B

AUyqspft…5WF2WW3f

18f29f67a1129f…7a53fb5149b9fe

2 in → 2 out10.5829 XPM340 B

AGzrd4MM…7HC9qVLn ALBUqcHz…qYwV25mJ

3a1d3d3230394d…fd6a2cbee0468f

1 in → 2 out4.6411 XPM227 B

AUPfJtPe…XVuYKCu4 AUfreQa4…MJnpJFaX

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.

1.062 × 10⁹⁷(98-digit number)

10624520052829661493…96116355571902054399

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

1.062 × 10⁹⁷(98-digit number)

10624520052829661493…96116355571902054399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.062 × 10⁹⁷(98-digit number)

10624520052829661493…96116355571902054401

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

2.124 × 10⁹⁷(98-digit number)

21249040105659322986…92232711143804108799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.124 × 10⁹⁷(98-digit number)

21249040105659322986…92232711143804108801

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

4.249 × 10⁹⁷(98-digit number)

42498080211318645973…84465422287608217599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.249 × 10⁹⁷(98-digit number)

42498080211318645973…84465422287608217601

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

8.499 × 10⁹⁷(98-digit number)

84996160422637291947…68930844575216435199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.499 × 10⁹⁷(98-digit number)

84996160422637291947…68930844575216435201

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

1.699 × 10⁹⁸(99-digit number)

16999232084527458389…37861689150432870399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.699 × 10⁹⁸(99-digit number)

16999232084527458389…37861689150432870401

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

3.399 × 10⁹⁸(99-digit number)

33998464169054916778…75723378300865740799

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 #2,739,736

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