Block #1,590,400

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/18/2016, 6:35:34 PM · Difficulty 10.6549 · 5,219,362 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

134304b44a9dd7d9cf59f196976e54df9bb25e9fcb97b72c95f68282989d98ca

View on Chainz ↗

Height

#1,590,400

Difficulty

10.654855

Transactions

Size

6.96 KB

Version

Bits

0aa7a493

Nonce

1,653,148,661

Timestamp

5/18/2016, 6:35:34 PM

Confirmations

5,219,362

Mined by

⛏️ P2SHANMg7yKAzKyCEvZHWGDsN8zfLz24UyxNdy

Merkle Root

6f11cdc6af19484fe882bb3b3549df76201e4ff368a6ab194ed8cecd6027a23d

Transactions (5)

Coinbase3967cf978200e9…01896271f8f608

1 in → 1 out8.8700 XPM109 B

ANMg7yKA…24UyxNdy

16f41dc91a8bc1…0563eb94b4f7a6

1 in → 32 out24.2297 XPM1.22 KB

AHpPuSR7…Sbim94bh AMXcYuE4…d7Th4jk6 AeD8xqD6…dbtEBDhN AGmCgDzF…7qjtnJE6 Af5eb8MS…1bzyujpA

318b7788de07db…a1544a20cc07fe

1 in → 51 out17.1677 XPM1.85 KB

AJ5u3Hok…zj9uSzXD Abf9bYnS…8bmRPE4d AMHmkapn…9LNmTuXS AUb8pcHH…C3pgmFZB AYeR4YEP…2CNonoT5

a7bd076d730554…5b69a17ad0b2ff

1 in → 51 out15.5852 XPM1.85 KB

ARbmELZZ…D2EmA9eK ARMMxjj1…3aJAcKcN AbiWDC4W…HNWnh6i1 AHdcBgRC…QMQBUujf AUAq2A6D…JCkXCNRL

9cd4313b94f355…5b7b6a5548aa76

1 in → 51 out0.9813 XPM1.85 KB

ARvfdQDN…ob2aPB2y AaQh1sFD…nQDvuTYJ AbpXgGFU…6cJV76dz AWLgNV3K…AKR3iepB AUS1wLVV…upJEAnCC

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.

2.694 × 10⁹⁷(98-digit number)

26940365575767572542…27997309783651123199

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

2.694 × 10⁹⁷(98-digit number)

26940365575767572542…27997309783651123199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.694 × 10⁹⁷(98-digit number)

26940365575767572542…27997309783651123201

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

5.388 × 10⁹⁷(98-digit number)

53880731151535145084…55994619567302246399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.388 × 10⁹⁷(98-digit number)

53880731151535145084…55994619567302246401

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

1.077 × 10⁹⁸(99-digit number)

10776146230307029016…11989239134604492799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.077 × 10⁹⁸(99-digit number)

10776146230307029016…11989239134604492801

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

2.155 × 10⁹⁸(99-digit number)

21552292460614058033…23978478269208985599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.155 × 10⁹⁸(99-digit number)

21552292460614058033…23978478269208985601

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

4.310 × 10⁹⁸(99-digit number)

43104584921228116067…47956956538417971199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.310 × 10⁹⁸(99-digit number)

43104584921228116067…47956956538417971201

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 #1,590,400

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