Block #2,697,557

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 6/9/2018, 12:37:58 AM · Difficulty 11.6543 · 4,133,249 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9ec8c9a779437b58267079923a16433be4ea8d6505f52ea1767925e3c16a95e1

View on Chainz ↗

Height

#2,697,557

Difficulty

11.654307

Transactions

Size

720 B

Version

Bits

0ba780a5

Nonce

2,122,141,309

Timestamp

6/9/2018, 12:37:58 AM

Confirmations

4,133,249

Mined by

⛏️ P2SHAJL7iWUyKz4WgepSYBkJG1B1LWanA94uQ3

Merkle Root

165a5893d1d95f80bbad7f77296690901ccbc4e3e080e7343affd6fe500433ea

Transactions (2)

Coinbasea56096c9742172…54f35103d6f6aa

1 in → 1 out7.3600 XPM110 B

AJL7iWUy…anA94uQ3

0ba5700f3c6228…840820ef791ae0

3 in → 2 out443.3779 XPM521 B

ARuaWjo8…j9LsnkHy ATLw4wqX…kGTEjXFm

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.

6.554 × 10⁹¹(92-digit number)

65542329320457253243…66622998345600101579

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

6.554 × 10⁹¹(92-digit number)

65542329320457253243…66622998345600101579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.554 × 10⁹¹(92-digit number)

65542329320457253243…66622998345600101581

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

1.310 × 10⁹²(93-digit number)

13108465864091450648…33245996691200203159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.310 × 10⁹²(93-digit number)

13108465864091450648…33245996691200203161

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

2.621 × 10⁹²(93-digit number)

26216931728182901297…66491993382400406319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.621 × 10⁹²(93-digit number)

26216931728182901297…66491993382400406321

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

5.243 × 10⁹²(93-digit number)

52433863456365802594…32983986764800812639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.243 × 10⁹²(93-digit number)

52433863456365802594…32983986764800812641

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

1.048 × 10⁹³(94-digit number)

10486772691273160518…65967973529601625279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.048 × 10⁹³(94-digit number)

10486772691273160518…65967973529601625281

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

2.097 × 10⁹³(94-digit number)

20973545382546321037…31935947059203250559

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

2.097 × 10⁹³(94-digit number)

20973545382546321037…31935947059203250561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,697,557

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