Block #2,634,058

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 6:01:12 PM · Difficulty 11.2207 · 4,209,337 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cdc101b653d834dacae7f4987c1ed88c383a77026646c091d470db1d33aa1a64

View on Chainz ↗

Height

#2,634,058

Difficulty

11.220713

Transactions

Size

1.06 KB

Version

Bits

0b3880a8

Nonce

1,967,531,352

Timestamp

4/28/2018, 6:01:12 PM

Confirmations

4,209,337

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

baa0996880e67bb4f35d16d8de815f0c8358523dc2b83dd70a3ea35613f0a88d

Transactions (3)

Coinbase885d2a806fc31f…4ab49c5e758b69

1 in → 1 out7.9500 XPM109 B

Adqah8zh…1WwoHJ9t

819a054868269b…32bd63aeace0ba

3 in → 6 out2394.5535 XPM659 B

ASk9H3sY…qUG8r1d4 APi8C85f…Lg5MDiei ARZVu2Xu…dnqxqk6T AQwQCJai…x2rDr9Lo AGq2Nru3…2dvKMDay

32c95113fa0044…27589881c3e5d5

1 in → 2 out246613.8362 XPM226 B

AWrEGZFD…UB4ETKW7 AUwXJkuX…2PqcCsPo

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.

1.639 × 10⁹⁴(95-digit number)

16393058631127496396…05564006640036916799

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

1.639 × 10⁹⁴(95-digit number)

16393058631127496396…05564006640036916799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.639 × 10⁹⁴(95-digit number)

16393058631127496396…05564006640036916801

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

3.278 × 10⁹⁴(95-digit number)

32786117262254992793…11128013280073833599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.278 × 10⁹⁴(95-digit number)

32786117262254992793…11128013280073833601

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

6.557 × 10⁹⁴(95-digit number)

65572234524509985586…22256026560147667199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.557 × 10⁹⁴(95-digit number)

65572234524509985586…22256026560147667201

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

1.311 × 10⁹⁵(96-digit number)

13114446904901997117…44512053120295334399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.311 × 10⁹⁵(96-digit number)

13114446904901997117…44512053120295334401

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

2.622 × 10⁹⁵(96-digit number)

26228893809803994234…89024106240590668799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.622 × 10⁹⁵(96-digit number)

26228893809803994234…89024106240590668801

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

5.245 × 10⁹⁵(96-digit number)

52457787619607988469…78048212481181337599

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 #2,634,058

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