Block #2,160,551

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/14/2017, 4:23:09 PM · Difficulty 10.9015 · 4,648,012 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9726a867a6eb775343a63ded5f96291dc74e1830718ab2ee2dfe6aadfcb353e3

View on Chainz ↗

Height

#2,160,551

Difficulty

10.901499

Transactions

Size

7.92 KB

Version

Bits

0ae6c89c

Nonce

424,186,087

Timestamp

6/14/2017, 4:23:09 PM

Confirmations

4,648,012

Mined by

⛏️ P2SHAMKrtKthCNajF3H9i7rX3P4rYLFrphYsCY

Merkle Root

c5c2bd5dd07cb6e57c610a4c701bb1cce6de16ffe3868a63000b28af076b820d

Transactions (2)

Coinbaseff56f7a53630f5…c22b969ea953bb

1 in → 1 out8.4800 XPM110 B

AMKrtKth…FrphYsCY

7dda42ef3243c9…9d21b857ed0de3

53 in → 2 out55.0637 XPM7.72 KB

AM6wkY1Z…tEaXBnAC ALkkPpHL…v5PkED9L

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.

5.170 × 10⁹³(94-digit number)

51701133968817446739…72509751022743521919

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

5.170 × 10⁹³(94-digit number)

51701133968817446739…72509751022743521919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.170 × 10⁹³(94-digit number)

51701133968817446739…72509751022743521921

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

1.034 × 10⁹⁴(95-digit number)

10340226793763489347…45019502045487043839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.034 × 10⁹⁴(95-digit number)

10340226793763489347…45019502045487043841

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

2.068 × 10⁹⁴(95-digit number)

20680453587526978695…90039004090974087679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.068 × 10⁹⁴(95-digit number)

20680453587526978695…90039004090974087681

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

4.136 × 10⁹⁴(95-digit number)

41360907175053957391…80078008181948175359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.136 × 10⁹⁴(95-digit number)

41360907175053957391…80078008181948175361

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

8.272 × 10⁹⁴(95-digit number)

82721814350107914783…60156016363896350719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.272 × 10⁹⁴(95-digit number)

82721814350107914783…60156016363896350721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,160,551

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