Block #2,591,700

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/29/2018, 8:07:22 PM · Difficulty 11.3224 · 4,252,770 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9257cdd563927e676b1e1ed4c1e9596b933658661eff4343976589ededcb5493

View on Chainz ↗

Height

#2,591,700

Difficulty

11.322353

Transactions

Size

561 B

Version

Bits

0b5285bd

Nonce

41,278,616

Timestamp

3/29/2018, 8:07:22 PM

Confirmations

4,252,770

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

0e9a8369d3c81230321855b24f4bdd242595b9a9d7aa19d07cac69766ffbc122

Transactions (2)

Coinbasee24f199c40bbe0…9b3739fbab2b00

1 in → 1 out7.8000 XPM110 B

Adqah8zh…1WwoHJ9t

a174d306859cb6…51a1d43de1a933

1 in → 6 out16.5213 XPM361 B

AYjENMYg…Cmrp3Tvo ALvm45yC…8A61g5Lv AJvpLvEU…2LinAVXj AXNLTRcT…4Nrdz3g3 AJ4UeLk6…gWW5VUcX

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.

4.134 × 10⁹⁴(95-digit number)

41342693422803078330…71536055755380053239

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

4.134 × 10⁹⁴(95-digit number)

41342693422803078330…71536055755380053239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.134 × 10⁹⁴(95-digit number)

41342693422803078330…71536055755380053241

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

8.268 × 10⁹⁴(95-digit number)

82685386845606156660…43072111510760106479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.268 × 10⁹⁴(95-digit number)

82685386845606156660…43072111510760106481

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

1.653 × 10⁹⁵(96-digit number)

16537077369121231332…86144223021520212959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.653 × 10⁹⁵(96-digit number)

16537077369121231332…86144223021520212961

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

3.307 × 10⁹⁵(96-digit number)

33074154738242462664…72288446043040425919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.307 × 10⁹⁵(96-digit number)

33074154738242462664…72288446043040425921

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

6.614 × 10⁹⁵(96-digit number)

66148309476484925328…44576892086080851839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.614 × 10⁹⁵(96-digit number)

66148309476484925328…44576892086080851841

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

1.322 × 10⁹⁶(97-digit number)

13229661895296985065…89153784172161703679

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 #2,591,700

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