Block #2,557,660

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/9/2018, 10:01:34 PM · Difficulty 10.9914 · 4,274,043 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7271dfb7cc4fcc06ccb310d8f17f2d55fe3e39a557261085a5d79c62b0542020

View on Chainz ↗

Height

#2,557,660

Difficulty

10.991426

Transactions

Size

573 B

Version

Bits

0afdce1b

Nonce

104,210,903

Timestamp

3/9/2018, 10:01:34 PM

Confirmations

4,274,043

Mined by

⛏️ P2SHARfbq4hb4JXgpwChFLhgN1HvDZJebys5LZ

Merkle Root

83ee6a73719a13be9323e8e54c1c008994d056e2c29c8b8c130dcb303c09c8ae

Transactions (2)

Coinbase65ee2f0520a18c…fe6392dbf3a46c

1 in → 1 out8.2700 XPM110 B

ARfbq4hb…Jebys5LZ

28bd7fcdd11f51…34b31979734df2

2 in → 2 out8.4163 XPM372 B

AUxYadQb…inUR4QFa AMMKxwmD…QawrVb8i

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.

4.913 × 10⁹⁶(97-digit number)

49132476405355285663…13043964234246955519

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

4.913 × 10⁹⁶(97-digit number)

49132476405355285663…13043964234246955519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.913 × 10⁹⁶(97-digit number)

49132476405355285663…13043964234246955521

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

9.826 × 10⁹⁶(97-digit number)

98264952810710571326…26087928468493911039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.826 × 10⁹⁶(97-digit number)

98264952810710571326…26087928468493911041

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

1.965 × 10⁹⁷(98-digit number)

19652990562142114265…52175856936987822079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.965 × 10⁹⁷(98-digit number)

19652990562142114265…52175856936987822081

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

3.930 × 10⁹⁷(98-digit number)

39305981124284228530…04351713873975644159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.930 × 10⁹⁷(98-digit number)

39305981124284228530…04351713873975644161

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

7.861 × 10⁹⁷(98-digit number)

78611962248568457061…08703427747951288319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.861 × 10⁹⁷(98-digit number)

78611962248568457061…08703427747951288321

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

1.572 × 10⁹⁸(99-digit number)

15722392449713691412…17406855495902576639

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 #2,557,660

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