Block #61,882

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 3:52:59 PM · Difficulty 8.9746 · 6,747,904 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

58dc665e18f4904fd11d460375af22790cfdcb6c3d3f1c4439689295e8cb22a5

View on Chainz ↗

Height

#61,882

Difficulty

8.974640

Transactions

Size

572 B

Version

Bits

08f98205

Nonce

767

Timestamp

7/18/2013, 3:52:59 PM

Confirmations

6,747,904

Mined by

⛏️ P2SHAJYRnqLmd6AgUCfBVPo12SbK5ou4A9qzv3

Merkle Root

df6afdf3f98058ad64a7d1393ccdd9f4db05546a212d437fd51708858bc23c44

Transactions (2)

Coinbaseb2bbb0be152f22…9122d97fc581a1

1 in → 1 out12.4100 XPM109 B

AJYRnqLm…u4A9qzv3

fe8fdbdc8a194b…452d6c424f89e3

2 in → 2 out198.2500 XPM374 B

AKziVusr…xxZkqarr ANQwJ4yG…31bDG4p5

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.

1.894 × 10⁹¹(92-digit number)

18941280812943107306…43826329517034002199

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

1.894 × 10⁹¹(92-digit number)

18941280812943107306…43826329517034002199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.894 × 10⁹¹(92-digit number)

18941280812943107306…43826329517034002201

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

3.788 × 10⁹¹(92-digit number)

37882561625886214613…87652659034068004399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.788 × 10⁹¹(92-digit number)

37882561625886214613…87652659034068004401

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

7.576 × 10⁹¹(92-digit number)

75765123251772429226…75305318068136008799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.576 × 10⁹¹(92-digit number)

75765123251772429226…75305318068136008801

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

1.515 × 10⁹²(93-digit number)

15153024650354485845…50610636136272017599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.515 × 10⁹²(93-digit number)

15153024650354485845…50610636136272017601

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

3.030 × 10⁹²(93-digit number)

30306049300708971690…01221272272544035199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #61,882

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