Block #2,476,057

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/16/2018, 5:52:55 PM · Difficulty 10.9644 · 4,367,397 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6c443602085361e9f64613c7b4db993820244a77cc73bfe93a942e2d3bbc0ac5

View on Chainz ↗

Height

#2,476,057

Difficulty

10.964355

Transactions

Size

990 B

Version

Bits

0af6dff4

Nonce

233,512,637

Timestamp

1/16/2018, 5:52:55 PM

Confirmations

4,367,397

Mined by

⛏️ P2SHAYhPFv6NZBGot3uz35PRARPZRee6Wij1oG

Merkle Root

d4f2e60ef986719185b1c5054f9f1ee0e35580a43f78cc67c89c08bf531810bd

Transactions (4)

Coinbasebb537691cc35e8…35901400bf4570

1 in → 1 out8.3300 XPM110 B

AYhPFv6N…e6Wij1oG

e9dd5ab0657a65…387aeaa3b84f90

2 in → 2 out12.6000 XPM339 B

AXAyQD25…gp9jT2xS AeHPpVSr…BNjUZcPp

2a0e8eafb6b4f2…bafc1eb556fde5

1 in → 2 out4.2900 XPM225 B

Af6HBJVa…GR2CnRRx ARetu55H…Q43vw1C4

062a4e0d02d5a4…a0b01b659695fb

1 in → 2 out4.2900 XPM226 B

AZ4wAM7R…b76w7QPp Af2J6BuG…H8ThkXpN

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.

5.838 × 10⁹⁴(95-digit number)

58386048425346075670…22655406645082867839

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

5.838 × 10⁹⁴(95-digit number)

58386048425346075670…22655406645082867839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.838 × 10⁹⁴(95-digit number)

58386048425346075670…22655406645082867841

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

1.167 × 10⁹⁵(96-digit number)

11677209685069215134…45310813290165735679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.167 × 10⁹⁵(96-digit number)

11677209685069215134…45310813290165735681

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

2.335 × 10⁹⁵(96-digit number)

23354419370138430268…90621626580331471359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.335 × 10⁹⁵(96-digit number)

23354419370138430268…90621626580331471361

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

4.670 × 10⁹⁵(96-digit number)

46708838740276860536…81243253160662942719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.670 × 10⁹⁵(96-digit number)

46708838740276860536…81243253160662942721

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

9.341 × 10⁹⁵(96-digit number)

93417677480553721072…62486506321325885439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.341 × 10⁹⁵(96-digit number)

93417677480553721072…62486506321325885441

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

1.868 × 10⁹⁶(97-digit number)

18683535496110744214…24973012642651770879

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 #2,476,057

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