Block #1,651,447

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/29/2016, 12:05:59 PM · Difficulty 10.7164 · 5,164,907 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1a91b88d5258b0ad1f021dd5abb40e0ecf50f496ec1a4a343b338207398ab0a3

View on Chainz ↗

Height

#1,651,447

Difficulty

10.716449

Transactions

Size

14.30 KB

Version

Bits

0ab7692c

Nonce

163,938,110

Timestamp

6/29/2016, 12:05:59 PM

Confirmations

5,164,907

Mined by

⛏️ P2SHALxBSt43xHo5ERcos66iqevGzUV9h7sJKE

Merkle Root

61c9e35184f3df44c5484b12ed3f380c050d98f81ca82fd34b50e1d1b9e6872d

Transactions (2)

Coinbase0595b1e632ecff…d5ed40c3e8b5ea

1 in → 1 out8.9000 XPM109 B

ALxBSt43…V9h7sJKE

f616eaa5167283…ff6aba3c711f36

97 in → 2 out16.0100 XPM14.10 KB

AKsii26n…kMwXuWUA AGyiGjWR…yy2Gk1HV

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.

9.332 × 10⁹³(94-digit number)

93323372138537106247…26751714745307863039

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

9.332 × 10⁹³(94-digit number)

93323372138537106247…26751714745307863039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.332 × 10⁹³(94-digit number)

93323372138537106247…26751714745307863041

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

1.866 × 10⁹⁴(95-digit number)

18664674427707421249…53503429490615726079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.866 × 10⁹⁴(95-digit number)

18664674427707421249…53503429490615726081

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

3.732 × 10⁹⁴(95-digit number)

37329348855414842498…07006858981231452159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.732 × 10⁹⁴(95-digit number)

37329348855414842498…07006858981231452161

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

7.465 × 10⁹⁴(95-digit number)

74658697710829684997…14013717962462904319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.465 × 10⁹⁴(95-digit number)

74658697710829684997…14013717962462904321

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

1.493 × 10⁹⁵(96-digit number)

14931739542165936999…28027435924925808639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.493 × 10⁹⁵(96-digit number)

14931739542165936999…28027435924925808641

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 #1,651,447

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