Block #2,699,127

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/10/2018, 4:54:15 AM · Difficulty 11.6457 · 4,144,214 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b8c630e71da864b247030a0249153152621661073d73aa6d17da64038fb111da

View on Chainz ↗

Height

#2,699,127

Difficulty

11.645668

Transactions

Size

8.57 KB

Version

Bits

0ba54a7c

Nonce

633,112,936

Timestamp

6/10/2018, 4:54:15 AM

Confirmations

4,144,214

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

4a9360882d99f084fd63d42ba78f1cc49861248fde24b48888562b01da955591

Transactions (4)

Coinbase502fd9d1a5bb60…cb848239653e5c

1 in → 1 out7.4600 XPM110 B

AZtxQr2F…7grUWrUz

232b47e16aaff5…77514704f2456d

69 in → 2 out504.5300 XPM7.79 KB

AJcDB81D…ZX2on3Cs AG1YWB3W…eaYyXigu

5e1ce9b59bb6e6…b66a5e7f5ef1ee

1 in → 2 out19.9600 XPM226 B

APVKWthF…PMMxwRoz AGehzdyA…RcjXDUWf

1cf4b43edd4b56…b1bdc8ae2c3615

2 in → 2 out19.8600 XPM374 B

ALFMKdF6…CwdGiSnU AH8UAN4u…zxwiJkLN

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.

1.689 × 10⁹⁶(97-digit number)

16896115708217674998…62905705828756495359

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

1.689 × 10⁹⁶(97-digit number)

16896115708217674998…62905705828756495359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.689 × 10⁹⁶(97-digit number)

16896115708217674998…62905705828756495361

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

3.379 × 10⁹⁶(97-digit number)

33792231416435349996…25811411657512990719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.379 × 10⁹⁶(97-digit number)

33792231416435349996…25811411657512990721

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

6.758 × 10⁹⁶(97-digit number)

67584462832870699992…51622823315025981439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.758 × 10⁹⁶(97-digit number)

67584462832870699992…51622823315025981441

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

1.351 × 10⁹⁷(98-digit number)

13516892566574139998…03245646630051962879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.351 × 10⁹⁷(98-digit number)

13516892566574139998…03245646630051962881

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

2.703 × 10⁹⁷(98-digit number)

27033785133148279996…06491293260103925759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.703 × 10⁹⁷(98-digit number)

27033785133148279996…06491293260103925761

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

5.406 × 10⁹⁷(98-digit number)

54067570266296559993…12982586520207851519

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 #2,699,127

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