Block #1,591,912

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/19/2016, 8:07:02 PM · Difficulty 10.6535 · 5,235,383 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99e64965b91ae50f46f8c3f7369cdb2452dc02ca8678749e846a300e7418dee8

View on Chainz ↗

Height

#1,591,912

Difficulty

10.653498

Transactions

Size

9.98 KB

Version

Bits

0aa74bad

Nonce

1,018,418,552

Timestamp

5/19/2016, 8:07:02 PM

Confirmations

5,235,383

Mined by

⛏️ P2SHAMzA6r3kA4qz4pukArvQRSKEZeWW6PKeRM

Merkle Root

96a5bb34ae2ae08b4cd9ca322ff2d78bbdb701e5ba9d20e1ca04c483e6d27dcf

Transactions (3)

Coinbase85c8465b265248…dd192e353d072b

1 in → 1 out8.9200 XPM110 B

AMzA6r3k…WW6PKeRM

35f91b91285b52…7e079b6565566d

59 in → 2 out1000.5900 XPM8.60 KB

Ab9mqhoZ…DwwJW1iN AZnLTnxW…xkUsRKda

73a6abb0d53bbc…a85579d2d3bc2d

1 in → 31 out133.1960 XPM1.18 KB

AZb72Xpi…jMwjS9yX AXG9Je3e…MnsGKCC5 APXuETT4…6e8fgsdf Acpy9Hyf…3VgvNDkf AWDqg9oU…m1tQfgwY

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.

3.592 × 10⁹³(94-digit number)

35923957768386013045…70276797360733242759

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

3.592 × 10⁹³(94-digit number)

35923957768386013045…70276797360733242759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.592 × 10⁹³(94-digit number)

35923957768386013045…70276797360733242761

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

7.184 × 10⁹³(94-digit number)

71847915536772026091…40553594721466485519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.184 × 10⁹³(94-digit number)

71847915536772026091…40553594721466485521

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

1.436 × 10⁹⁴(95-digit number)

14369583107354405218…81107189442932971039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.436 × 10⁹⁴(95-digit number)

14369583107354405218…81107189442932971041

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

2.873 × 10⁹⁴(95-digit number)

28739166214708810436…62214378885865942079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.873 × 10⁹⁴(95-digit number)

28739166214708810436…62214378885865942081

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

5.747 × 10⁹⁴(95-digit number)

57478332429417620873…24428757771731884159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.747 × 10⁹⁴(95-digit number)

57478332429417620873…24428757771731884161

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 #1,591,912

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