Block #1,567,039

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/1/2016, 7:05:44 AM · Difficulty 10.7582 · 5,250,276 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

580647dce0497f9a2cec16394de9360590d3597355ad9668817ed6beda38887f

View on Chainz ↗

Height

#1,567,039

Difficulty

10.758228

Transactions

Size

969 B

Version

Bits

0ac21b39

Nonce

837,594,093

Timestamp

5/1/2016, 7:05:44 AM

Confirmations

5,250,276

Mined by

⛏️ P2SHAKX5Xh1PG1Q291YWrdtDw4wVvVpZSDavFc

Merkle Root

0e6b040e5dc5b68c48bff513ba51298415ba4bc4f1639386d485717142d8bc62

Transactions (2)

Coinbase0fe61aed4ac387…ce661299475a87

1 in → 1 out8.6400 XPM109 B

AKX5Xh1P…pZSDavFc

f2cb0efdd311a6…92e40324e54a6d

1 in → 18 out191.0250 XPM769 B

AKuWnoR8…TaAkbxkM Aejy7AaU…d2cWkHZD AMUNeiYe…j5vRhZJp AJ5nsAv9…mUnSKALU AP392vP6…HbBn1wjy

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.

1.451 × 10⁹⁷(98-digit number)

14510547167741980326…88085039037708185599

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

1.451 × 10⁹⁷(98-digit number)

14510547167741980326…88085039037708185599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.451 × 10⁹⁷(98-digit number)

14510547167741980326…88085039037708185601

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

2.902 × 10⁹⁷(98-digit number)

29021094335483960653…76170078075416371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.902 × 10⁹⁷(98-digit number)

29021094335483960653…76170078075416371201

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

5.804 × 10⁹⁷(98-digit number)

58042188670967921306…52340156150832742399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.804 × 10⁹⁷(98-digit number)

58042188670967921306…52340156150832742401

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

1.160 × 10⁹⁸(99-digit number)

11608437734193584261…04680312301665484799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.160 × 10⁹⁸(99-digit number)

11608437734193584261…04680312301665484801

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

2.321 × 10⁹⁸(99-digit number)

23216875468387168522…09360624603330969599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.321 × 10⁹⁸(99-digit number)

23216875468387168522…09360624603330969601

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 #1,567,039

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