Block #2,732,714

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/3/2018, 4:17:33 PM · Difficulty 11.6311 · 4,106,331 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f58f424e5bbe01742bcb26336c8d2a3baf6c04f2ca07b0d5fd4583913bf144a5

View on Chainz ↗

Height

#2,732,714

Difficulty

11.631111

Transactions

Size

1.00 KB

Version

Bits

0ba1907d

Nonce

401,651,888

Timestamp

7/3/2018, 4:17:33 PM

Confirmations

4,106,331

Mined by

⛏️ P2SHAUMFSC9La4kQkKsscMppbYZnaoEf8qGmRa

Merkle Root

2047bdcf7c7250e6f92f9bf27b24272708bfd9608eb859bbe2ed4d73c5e296e2

Transactions (3)

Coinbaseefddcdd46890c8…c8bd54cf73d44d

1 in → 1 out7.4000 XPM110 B

AUMFSC9L…Ef8qGmRa

5d8fb4095b24be…46a1b7676d6855

2 in → 2 out12.2000 XPM339 B

AbXFABGh…AWpYJ77c Aa4rTSPF…wZiX49Px

31e15b4015974b…7fc07a4749c70c

3 in → 2 out11.7200 XPM487 B

Ae1W14EW…L5HtFgd4 AcXtoaKv…4oXYPT9v

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.

1.963 × 10⁹⁵(96-digit number)

19639321176064286902…88443125537250982399

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

1.963 × 10⁹⁵(96-digit number)

19639321176064286902…88443125537250982399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.963 × 10⁹⁵(96-digit number)

19639321176064286902…88443125537250982401

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

3.927 × 10⁹⁵(96-digit number)

39278642352128573804…76886251074501964799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.927 × 10⁹⁵(96-digit number)

39278642352128573804…76886251074501964801

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

7.855 × 10⁹⁵(96-digit number)

78557284704257147608…53772502149003929599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.855 × 10⁹⁵(96-digit number)

78557284704257147608…53772502149003929601

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

1.571 × 10⁹⁶(97-digit number)

15711456940851429521…07545004298007859199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.571 × 10⁹⁶(97-digit number)

15711456940851429521…07545004298007859201

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

3.142 × 10⁹⁶(97-digit number)

31422913881702859043…15090008596015718399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.142 × 10⁹⁶(97-digit number)

31422913881702859043…15090008596015718401

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

6.284 × 10⁹⁶(97-digit number)

62845827763405718086…30180017192031436799

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 #2,732,714

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