Block #2,853,104

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 9/24/2018, 9:22:13 AM · Difficulty 11.7179 · 3,989,847 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

acfd767431aba49a22d7cb399e7440c06de90875480861e659fd99a9999c106c

View on Chainz ↗

Height

#2,853,104

Difficulty

11.717863

Transactions

Size

1.72 KB

Version

Bits

0bb7c5de

Nonce

1,227,399,147

Timestamp

9/24/2018, 9:22:13 AM

Confirmations

3,989,847

Mined by

⛏️ P2SHAUKPv6iaFoWwtbUFankYWWzRTEHaWXSVPS

Merkle Root

9ca448abb45fb26f1f7e670be8791a2bfaf112e5a0df4c5d5c727d7f52f5e562

Transactions (5)

Coinbased0acc254495527…6a48e571949c5a

1 in → 1 out7.3100 XPM110 B

AUKPv6ia…HaWXSVPS

dd7900e0f50820…b68cc7f08f5e34

2 in → 2 out14.6600 XPM307 B

AJ43HoDZ…hcMCuoDo AYGchnep…aKZEsSy4

e2efbe6c56167a…bbcf16c2399abc

2 in → 2 out14.5100 XPM306 B

AJ2gtkaa…u2kkSHoz APVKWthF…PMMxwRoz

510280b7f89849…3f7d10022af723

2 in → 2 out14.5100 XPM307 B

ANEq6Gdi…Pbk4HtRv AP1CP14p…kmh3WFAS

983de2710ea194…a89def92350213

4 in → 1 out10.0000 XPM636 B

Aek7aQzY…4495YRvK

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.

9.140 × 10⁹⁵(96-digit number)

91403444148499563127…74147297050008755199

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

9.140 × 10⁹⁵(96-digit number)

91403444148499563127…74147297050008755199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.140 × 10⁹⁵(96-digit number)

91403444148499563127…74147297050008755201

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

1.828 × 10⁹⁶(97-digit number)

18280688829699912625…48294594100017510399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.828 × 10⁹⁶(97-digit number)

18280688829699912625…48294594100017510401

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

3.656 × 10⁹⁶(97-digit number)

36561377659399825251…96589188200035020799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.656 × 10⁹⁶(97-digit number)

36561377659399825251…96589188200035020801

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

7.312 × 10⁹⁶(97-digit number)

73122755318799650502…93178376400070041599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.312 × 10⁹⁶(97-digit number)

73122755318799650502…93178376400070041601

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

1.462 × 10⁹⁷(98-digit number)

14624551063759930100…86356752800140083199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.462 × 10⁹⁷(98-digit number)

14624551063759930100…86356752800140083201

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

2.924 × 10⁹⁷(98-digit number)

29249102127519860200…72713505600280166399

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

2.924 × 10⁹⁷(98-digit number)

29249102127519860200…72713505600280166401

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 #2,853,104

Cookie Preferences