Block #1,437,838

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/1/2016, 12:03:25 AM · Difficulty 10.7910 · 5,401,837 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f18c1744c11e8dd3da3313b4bd7be6c60027ced78cb8c55263e13113129c14f8

View on Chainz ↗

Height

#1,437,838

Difficulty

10.790967

Transactions

Size

868 B

Version

Bits

0aca7cd1

Nonce

473,134,079

Timestamp

2/1/2016, 12:03:25 AM

Confirmations

5,401,837

Mined by

⛏️ P2SHAatSu7x2cPLJEnDYAXdcq891xqmpQAPVr9

Merkle Root

fd04c439c56d411fda44381043083d2e9061475e4701e9c640947f36377ded2a

Transactions (2)

Coinbase6b859ad1910422…d79f6ba033ad3d

1 in → 1 out8.5800 XPM110 B

AatSu7x2…mpQAPVr9

d75da80a697e75…370a931cb7cbe9

1 in → 15 out119.0323 XPM667 B

ANyDEapF…RDDKga26 AKJWP64b…xFn4ggkM ALekHbnf…r2DWhBVp Acz74vFY…J4b7m3Hf AVjBizVs…tVDrfWHQ

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.

2.233 × 10⁹⁷(98-digit number)

22339528378485656159…95979259053366015999

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

2.233 × 10⁹⁷(98-digit number)

22339528378485656159…95979259053366015999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.233 × 10⁹⁷(98-digit number)

22339528378485656159…95979259053366016001

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

4.467 × 10⁹⁷(98-digit number)

44679056756971312318…91958518106732031999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.467 × 10⁹⁷(98-digit number)

44679056756971312318…91958518106732032001

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

8.935 × 10⁹⁷(98-digit number)

89358113513942624636…83917036213464063999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.935 × 10⁹⁷(98-digit number)

89358113513942624636…83917036213464064001

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

1.787 × 10⁹⁸(99-digit number)

17871622702788524927…67834072426928127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.787 × 10⁹⁸(99-digit number)

17871622702788524927…67834072426928128001

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

3.574 × 10⁹⁸(99-digit number)

35743245405577049854…35668144853856255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.574 × 10⁹⁸(99-digit number)

35743245405577049854…35668144853856256001

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 #1,437,838

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