Block #2,852,078

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/23/2018, 2:31:00 PM · Difficulty 11.7236 · 3,979,842 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a6e87de1d5eba7972633ec5c75e2d4ed5840c3f0da64f6b5c256319bbd1090ea

View on Chainz ↗

Height

#2,852,078

Difficulty

11.723641

Transactions

Size

1.45 KB

Version

Bits

0bb94084

Nonce

85,381,822

Timestamp

9/23/2018, 2:31:00 PM

Confirmations

3,979,842

Mined by

⛏️ P2SHAeGBmb72MrSKpNBC3Weqh3EH4bFzRdEpZy

Merkle Root

53bd0e27629a3cbaf697ae9fae00ac94e8a37e1dee6bca9f02b839a48e6e3baf

Transactions (4)

Coinbase2e8eb4a7291909…dcd74835755542

1 in → 1 out7.3000 XPM110 B

AeGBmb72…FzRdEpZy

e1dd5902f3dec5…ad9a93fff5e85b

6 in → 2 out30.0334 XPM831 B

ANz65jvR…vu7Ymacm AHfA8JdF…y7ueZthw

83221b44abfff3…ae21888cce152d

1 in → 2 out2.6418 XPM226 B

ARBpgiLR…emVivKnJ AVWMi3xJ…vCrqVoPz

5e997b46f92563…a6c36e597d06be

1 in → 2 out1.7274 XPM227 B

AVwU67nW…AqPc5xhQ AaxCraKt…CEBafb4N

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.

1.095 × 10⁹⁵(96-digit number)

10957547387124901121…62619861778955673599

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

1.095 × 10⁹⁵(96-digit number)

10957547387124901121…62619861778955673599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.095 × 10⁹⁵(96-digit number)

10957547387124901121…62619861778955673601

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

2.191 × 10⁹⁵(96-digit number)

21915094774249802242…25239723557911347199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.191 × 10⁹⁵(96-digit number)

21915094774249802242…25239723557911347201

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

4.383 × 10⁹⁵(96-digit number)

43830189548499604484…50479447115822694399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.383 × 10⁹⁵(96-digit number)

43830189548499604484…50479447115822694401

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

8.766 × 10⁹⁵(96-digit number)

87660379096999208969…00958894231645388799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.766 × 10⁹⁵(96-digit number)

87660379096999208969…00958894231645388801

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

1.753 × 10⁹⁶(97-digit number)

17532075819399841793…01917788463290777599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.753 × 10⁹⁶(97-digit number)

17532075819399841793…01917788463290777601

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

3.506 × 10⁹⁶(97-digit number)

35064151638799683587…03835576926581555199

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 #2,852,078

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