Block #416,097

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/23/2014, 4:48:03 AM · Difficulty 10.3989 · 6,392,880 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43c81e06c043246bd915b5809c17462821443c85f16ed75bc806f39a1154db14

View on Chainz ↗

Height

#416,097

Difficulty

10.398871

Transactions

Size

2.01 KB

Version

Bits

0a661c6f

Nonce

104,306

Timestamp

2/23/2014, 4:48:03 AM

Confirmations

6,392,880

Mined by

⛏️ aY^AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

b174fb96420c9075a90a2f2857464e05cbc105869607288b94856c34233d993d

Transactions (4)

Coinbase0edd528e100339…1e204d9f9730ce

1 in → 2 out9.2700 XPM131 B

AMVf7Jrg…xd5AVR7C AJno7LX2…vo4wdWtY

fb2623461d532a…69268b8706e2e1

6 in → 16 out55.1900 XPM1.21 KB

AeKNrjNj…1NEq95Ta ARBbV4XN…NKu8PUHX ALKgih3X…yaVE74WK ARvgDRHr…dYLY5cr4 AV2nLHtF…WTtiSvem

8bd9a26b67edac…73b4ec5b23519f

2 in → 2 out13.2150 XPM374 B

AWYCJLeN…bANCcKQT AWRhfQVH…qea81sAw

e78d287d4cb158…775c8ccc4a14db

1 in → 2 out7.1312 XPM227 B

AThAkSeT…LNmHgPc6 AM7HrnvZ…8R7L4ies

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.

4.167 × 10¹⁰²(103-digit number)

41679365773046031466…94677915591757579519

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

4.167 × 10¹⁰²(103-digit number)

41679365773046031466…94677915591757579519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.167 × 10¹⁰²(103-digit number)

41679365773046031466…94677915591757579521

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

8.335 × 10¹⁰²(103-digit number)

83358731546092062932…89355831183515159039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.335 × 10¹⁰²(103-digit number)

83358731546092062932…89355831183515159041

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

1.667 × 10¹⁰³(104-digit number)

16671746309218412586…78711662367030318079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.667 × 10¹⁰³(104-digit number)

16671746309218412586…78711662367030318081

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

3.334 × 10¹⁰³(104-digit number)

33343492618436825172…57423324734060636159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.334 × 10¹⁰³(104-digit number)

33343492618436825172…57423324734060636161

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

6.668 × 10¹⁰³(104-digit number)

66686985236873650345…14846649468121272319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.668 × 10¹⁰³(104-digit number)

66686985236873650345…14846649468121272321

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 #416,097

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