Block #2,618,014

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/17/2018, 1:07:26 PM · Difficulty 11.2337 · 4,215,682 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5cfe56995253546a37fe3652e583b3a92325bf996a9d0512f2f791241e3a2e6

View on Chainz ↗

Height

#2,618,014

Difficulty

11.233693

Transactions

Size

427 B

Version

Bits

0b3bd356

Nonce

396,934,372

Timestamp

4/17/2018, 1:07:26 PM

Confirmations

4,215,682

Mined by

⛏️ P2SHAeKNh3d76KDkXueo8UNjuvRgazi12xCgmt

Merkle Root

c1a586812a43b7e616b7eba3e91cf2f476fec96cc3c2c04e4a86e47d964eba5d

Transactions (2)

Coinbasef087c45c7c43af…97a70904ea60a2

1 in → 1 out7.9200 XPM110 B

AeKNh3d7…i12xCgmt

973b0bf32db4f7…5723d9feda4c95

1 in → 2 out7.9800 XPM227 B

AGhzcDHG…MZv6XCbm AYWtGVsm…ymWkSfEy

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.

1.454 × 10⁹⁵(96-digit number)

14543638026744186685…93639583817945238719

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

1.454 × 10⁹⁵(96-digit number)

14543638026744186685…93639583817945238719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.454 × 10⁹⁵(96-digit number)

14543638026744186685…93639583817945238721

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

2.908 × 10⁹⁵(96-digit number)

29087276053488373370…87279167635890477439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.908 × 10⁹⁵(96-digit number)

29087276053488373370…87279167635890477441

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

5.817 × 10⁹⁵(96-digit number)

58174552106976746741…74558335271780954879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.817 × 10⁹⁵(96-digit number)

58174552106976746741…74558335271780954881

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

1.163 × 10⁹⁶(97-digit number)

11634910421395349348…49116670543561909759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.163 × 10⁹⁶(97-digit number)

11634910421395349348…49116670543561909761

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

2.326 × 10⁹⁶(97-digit number)

23269820842790698696…98233341087123819519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.326 × 10⁹⁶(97-digit number)

23269820842790698696…98233341087123819521

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

4.653 × 10⁹⁶(97-digit number)

46539641685581397393…96466682174247639039

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 #2,618,014

Cookie Preferences