Block #1,610,766

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/2/2016, 9:25:34 AM · Difficulty 10.6055 · 5,222,727 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d8bb65115d6a2efe618f706d6897be9a437d156c9be3983c09f396edb833ff46

View on Chainz ↗

Height

#1,610,766

Difficulty

10.605479

Transactions

Size

1.04 KB

Version

Bits

0a9b00ad

Nonce

651,304,207

Timestamp

6/2/2016, 9:25:34 AM

Confirmations

5,222,727

Mined by

⛏️ P2SHAeujpnxYdfdtiKchyfiqNdpMNMvVeBFyxx

Merkle Root

6ef9d16b7dd53fde8f72d7cae37bfa082ef43281fe16a2dad32b241d62983b50

Transactions (2)

Coinbase257032fe83114c…607f8ab5b4baa1

1 in → 1 out8.8900 XPM109 B

AeujpnxY…vVeBFyxx

27fac23fb3c0ce…81a4a1bdfb6e44

1 in → 21 out153.3153 XPM872 B

AafCLqqv…EeFxBfBr AUs4CL1f…dg6BsdQi AFpQivJb…kvWEgNnC AHLrfMCb…5eE2yTTn AehBPrw4…RMbC68Fk

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.

2.163 × 10⁹²(93-digit number)

21635710580388856505…23827764618684780559

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

2.163 × 10⁹²(93-digit number)

21635710580388856505…23827764618684780559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.163 × 10⁹²(93-digit number)

21635710580388856505…23827764618684780561

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

4.327 × 10⁹²(93-digit number)

43271421160777713010…47655529237369561119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.327 × 10⁹²(93-digit number)

43271421160777713010…47655529237369561121

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

8.654 × 10⁹²(93-digit number)

86542842321555426020…95311058474739122239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.654 × 10⁹²(93-digit number)

86542842321555426020…95311058474739122241

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

1.730 × 10⁹³(94-digit number)

17308568464311085204…90622116949478244479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.730 × 10⁹³(94-digit number)

17308568464311085204…90622116949478244481

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

3.461 × 10⁹³(94-digit number)

34617136928622170408…81244233898956488959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.461 × 10⁹³(94-digit number)

34617136928622170408…81244233898956488961

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 #1,610,766

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