Block #2,655,609

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/10/2018, 8:03:28 AM · Difficulty 11.7041 · 4,187,483 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d45b5bc5dd7f0dc14a296e7250c2d53cf45ba944e8a00ddd149e45e95709e705

View on Chainz ↗

Height

#2,655,609

Difficulty

11.704055

Transactions

Size

1.94 KB

Version

Bits

0bb43cf4

Nonce

1,588,901,135

Timestamp

5/10/2018, 8:03:28 AM

Confirmations

4,187,483

Mined by

⛏️ P2SHAGR5xjhkQCYwWmMSeaKqmNuGihVm5xxfoo

Merkle Root

e4ab983d51f0c7d76c9c6747da50f572a68f0bdbe68cdd6677e252c09c1978ac

Transactions (3)

Coinbase9d863739386b90…779b794aef775e

1 in → 1 out7.3100 XPM110 B

AGR5xjhk…Vm5xxfoo

7dc974c26ff01f…ed4246c0e56ac8

5 in → 2 out372.9566 XPM816 B

ASC9um3f…YLq9NmQu AZ11SwEy…s7qssZyS

fc8ca7f739ff16…f5ecd3f4af4e7d

6 in → 2 out345.2831 XPM967 B

AJdM6BQD…g1g59wty AYpGMJy4…TXxUMxyV

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.

1.975 × 10⁹⁷(98-digit number)

19755111717943419462…19208157716110786559

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

1.975 × 10⁹⁷(98-digit number)

19755111717943419462…19208157716110786559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.975 × 10⁹⁷(98-digit number)

19755111717943419462…19208157716110786561

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

3.951 × 10⁹⁷(98-digit number)

39510223435886838924…38416315432221573119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.951 × 10⁹⁷(98-digit number)

39510223435886838924…38416315432221573121

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

7.902 × 10⁹⁷(98-digit number)

79020446871773677848…76832630864443146239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.902 × 10⁹⁷(98-digit number)

79020446871773677848…76832630864443146241

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

1.580 × 10⁹⁸(99-digit number)

15804089374354735569…53665261728886292479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.580 × 10⁹⁸(99-digit number)

15804089374354735569…53665261728886292481

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

3.160 × 10⁹⁸(99-digit number)

31608178748709471139…07330523457772584959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.160 × 10⁹⁸(99-digit number)

31608178748709471139…07330523457772584961

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

6.321 × 10⁹⁸(99-digit number)

63216357497418942279…14661046915545169919

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 #2,655,609

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