Block #1,573,522

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/6/2016, 9:06:35 AM · Difficulty 10.7147 · 5,260,251 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ae1165f9166ef8464e4f62ff2c9ce313fcbaea43b4fdace7b6c5c8fb4b59423a

View on Chainz ↗

Height

#1,573,522

Difficulty

10.714712

Transactions

Size

902 B

Version

Bits

0ab6f756

Nonce

1,113,495,898

Timestamp

5/6/2016, 9:06:35 AM

Confirmations

5,260,251

Mined by

⛏️ P2SHAUYXS2vAzHrtUQLNhVDJmsN7k4WEujQawV

Merkle Root

bc38de002e19dddb4530ec78778738260b797e233de4fb6a1e807d1ce560eae8

Transactions (2)

Coinbase8f54358185136d…3f4b4bc562e8f9

1 in → 1 out8.7100 XPM109 B

AUYXS2vA…WEujQawV

1bd5e47521fd0a…6486c29fa1ddc8

1 in → 16 out98.1839 XPM702 B

AcBYJJw6…if25JnRf AN9TY3x5…eX14vkom AVvD3Wa4…rt7ACfXc AJrpEg1W…koapTd3C AZWtzmDz…xdn2rWNM

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.

2.850 × 10⁹⁶(97-digit number)

28505301950309365686…33626547912263280639

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

2.850 × 10⁹⁶(97-digit number)

28505301950309365686…33626547912263280639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.850 × 10⁹⁶(97-digit number)

28505301950309365686…33626547912263280641

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

5.701 × 10⁹⁶(97-digit number)

57010603900618731372…67253095824526561279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.701 × 10⁹⁶(97-digit number)

57010603900618731372…67253095824526561281

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

1.140 × 10⁹⁷(98-digit number)

11402120780123746274…34506191649053122559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.140 × 10⁹⁷(98-digit number)

11402120780123746274…34506191649053122561

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

2.280 × 10⁹⁷(98-digit number)

22804241560247492549…69012383298106245119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.280 × 10⁹⁷(98-digit number)

22804241560247492549…69012383298106245121

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

4.560 × 10⁹⁷(98-digit number)

45608483120494985098…38024766596212490239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.560 × 10⁹⁷(98-digit number)

45608483120494985098…38024766596212490241

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 #1,573,522

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