Block #1,589,191

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/17/2016, 11:05:59 PM · Difficulty 10.6520 · 5,247,155 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d64aec3f51fdcd13fc2a18880321a6bcd92b46794277699018f13158b6cd69cc

View on Chainz ↗

Height

#1,589,191

Difficulty

10.652012

Transactions

Size

1004 B

Version

Bits

0aa6ea40

Nonce

374,110,666

Timestamp

5/17/2016, 11:05:59 PM

Confirmations

5,247,155

Mined by

⛏️ P2SHAaKdJxxNUk7eUNgAcb2mxD8nd3wskC4vDn

Merkle Root

e536f9577790707b437d9b747d84836ff904dd9fcd4f22fc113ff36b73c4a8da

Transactions (2)

Coinbase4457bea1d0f0c6…72599b3a8e833f

1 in → 1 out8.8100 XPM109 B

AaKdJxxN…wskC4vDn

25024669e133d9…a0c360ba138e55

1 in → 19 out5.3788 XPM804 B

Ae9wYuZx…WqNFE1D7 AN9TY3x5…eX14vkom AW1UezKJ…yyWeSMc5 ARSGwfvq…RdvnptaP Ae8728TZ…4DMaZLBe

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.

9.700 × 10⁹⁷(98-digit number)

97001784593364318409…14806310047998279679

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

9.700 × 10⁹⁷(98-digit number)

97001784593364318409…14806310047998279679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.700 × 10⁹⁷(98-digit number)

97001784593364318409…14806310047998279681

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

1.940 × 10⁹⁸(99-digit number)

19400356918672863681…29612620095996559359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.940 × 10⁹⁸(99-digit number)

19400356918672863681…29612620095996559361

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

3.880 × 10⁹⁸(99-digit number)

38800713837345727363…59225240191993118719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.880 × 10⁹⁸(99-digit number)

38800713837345727363…59225240191993118721

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

7.760 × 10⁹⁸(99-digit number)

77601427674691454727…18450480383986237439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.760 × 10⁹⁸(99-digit number)

77601427674691454727…18450480383986237441

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

1.552 × 10⁹⁹(100-digit number)

15520285534938290945…36900960767972474879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.552 × 10⁹⁹(100-digit number)

15520285534938290945…36900960767972474881

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 #1,589,191

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