Block #2,953,464

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/5/2018, 6:09:15 PM · Difficulty 11.4000 · 3,888,041 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1089a04aec0ddc1fc694982611680f8ff6af7361fc013f7aff72034846b50079

View on Chainz ↗

Height

#2,953,464

Difficulty

11.399982

Transactions

Size

11.34 KB

Version

Bits

0b666536

Nonce

1,952,457,912

Timestamp

12/5/2018, 6:09:15 PM

Confirmations

3,888,041

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

294162c5bff644a09d81fc5886da600915046b9cc60affc3be328d72ca7ff6f8

Transactions (5)

Coinbasee04710d7239147…2030c4bd43ec69

1 in → 1 out7.8200 XPM110 B

AbXwmGxD…4XXYP765

1e79b6253b3643…a5470e54babeca

70 in → 2 out276.1200 XPM10.18 KB

AQRn6yfR…z5FsKtdj AWZGrDgh…dj84WNdN

757645c3ea1fdd…cf30e81611e6c8

2 in → 2 out15.5100 XPM307 B

AW3QZZmg…j2rGjUkp Aeopx6Fy…qUwEq1RK

216584b468b797…c6d6d070fb6ebc

2 in → 2 out15.3700 XPM305 B

AK8WnRTW…UgMPVH16 ASYezxNd…uerEgrAq

123d691ee25530…9a734999d63cd7

2 in → 2 out10.8700 XPM374 B

AH4dzyDX…zzaPrAvT APVKWthF…PMMxwRoz

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.

2.646 × 10⁹⁵(96-digit number)

26463478520671843058…62088595382001341959

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

2.646 × 10⁹⁵(96-digit number)

26463478520671843058…62088595382001341959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.646 × 10⁹⁵(96-digit number)

26463478520671843058…62088595382001341961

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

5.292 × 10⁹⁵(96-digit number)

52926957041343686116…24177190764002683919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.292 × 10⁹⁵(96-digit number)

52926957041343686116…24177190764002683921

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

1.058 × 10⁹⁶(97-digit number)

10585391408268737223…48354381528005367839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.058 × 10⁹⁶(97-digit number)

10585391408268737223…48354381528005367841

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

2.117 × 10⁹⁶(97-digit number)

21170782816537474446…96708763056010735679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.117 × 10⁹⁶(97-digit number)

21170782816537474446…96708763056010735681

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

4.234 × 10⁹⁶(97-digit number)

42341565633074948892…93417526112021471359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.234 × 10⁹⁶(97-digit number)

42341565633074948892…93417526112021471361

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

8.468 × 10⁹⁶(97-digit number)

84683131266149897785…86835052224042942719

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 #2,953,464

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