Block #1,497,786

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2016, 12:10:09 PM · Difficulty 10.6459 · 5,347,116 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1e4987ae7f1b3b8873c89d85685ee0379263d1c1f7c23f5058b374e26154cb13

View on Chainz ↗

Height

#1,497,786

Difficulty

10.645872

Transactions

Size

1.08 KB

Version

Bits

0aa557df

Nonce

116,438,653

Timestamp

3/15/2016, 12:10:09 PM

Confirmations

5,347,116

Mined by

⛏️ P2SHARSqELBsx1fk93KXWgZJD6szeFhg81pvB1

Merkle Root

6d85fcd8de30367128aa7913863a7cc39b10aead0b4fc4ac4f3ea06aaf3f0053

Transactions (2)

Coinbase6a693b5407035a…bd085ebbe5e499

1 in → 1 out8.8200 XPM110 B

ARSqELBs…hg81pvB1

de0715ef8074a1…b7df21c77e0877

1 in → 22 out98.7933 XPM905 B

AVamNxSv…j52o4ED9 AYpaQCPA…nWofibap ATyyatFN…YMychM5g AZ2Dv6vs…YoKVyFme AZGu2LFf…R1xomEtn

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.

4.899 × 10⁹⁴(95-digit number)

48999011315785657521…08695063942444844799

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

4.899 × 10⁹⁴(95-digit number)

48999011315785657521…08695063942444844799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.899 × 10⁹⁴(95-digit number)

48999011315785657521…08695063942444844801

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

9.799 × 10⁹⁴(95-digit number)

97998022631571315043…17390127884889689599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.799 × 10⁹⁴(95-digit number)

97998022631571315043…17390127884889689601

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

1.959 × 10⁹⁵(96-digit number)

19599604526314263008…34780255769779379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.959 × 10⁹⁵(96-digit number)

19599604526314263008…34780255769779379201

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

3.919 × 10⁹⁵(96-digit number)

39199209052628526017…69560511539558758399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.919 × 10⁹⁵(96-digit number)

39199209052628526017…69560511539558758401

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

7.839 × 10⁹⁵(96-digit number)

78398418105257052034…39121023079117516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.839 × 10⁹⁵(96-digit number)

78398418105257052034…39121023079117516801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #1,497,786

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