Block #2,160,744

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/14/2017, 7:27:26 PM · Difficulty 10.9017 · 4,682,100 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c8559513584a6db9f142ac2e9f815c3743a8bcecdd156c4c83df0f1ed9e578d

View on Chainz ↗

Height

#2,160,744

Difficulty

10.901695

Transactions

Size

2.29 KB

Version

Bits

0ae6d57d

Nonce

971,970,442

Timestamp

6/14/2017, 7:27:26 PM

Confirmations

4,682,100

Mined by

⛏️ P2SHAXTbCxcDAfZ5bkELmnJr1VmxHeASKW55Zz

Merkle Root

e41eee8aa89fb9269d26ffc2ccfa097cdd0b8d2a154f279cf639dba946d80afa

Transactions (2)

Coinbasee49bb566ea0754…fa693649c42c5c

1 in → 1 out8.4800 XPM110 B

AXTbCxcD…ASKW55Zz

8fd129538061d5…d81f92b9499cb7

14 in → 2 out217.0310 XPM2.10 KB

AeHTdHo5…yhroq7an AMh4G9Sj…B7MepdJ4

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.

8.701 × 10⁹⁸(99-digit number)

87013925858419939945…34285272185028607999

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

8.701 × 10⁹⁸(99-digit number)

87013925858419939945…34285272185028607999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.701 × 10⁹⁸(99-digit number)

87013925858419939945…34285272185028608001

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

1.740 × 10⁹⁹(100-digit number)

17402785171683987989…68570544370057215999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.740 × 10⁹⁹(100-digit number)

17402785171683987989…68570544370057216001

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

3.480 × 10⁹⁹(100-digit number)

34805570343367975978…37141088740114431999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.480 × 10⁹⁹(100-digit number)

34805570343367975978…37141088740114432001

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

6.961 × 10⁹⁹(100-digit number)

69611140686735951956…74282177480228863999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.961 × 10⁹⁹(100-digit number)

69611140686735951956…74282177480228864001

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

1.392 × 10¹⁰⁰(101-digit number)

13922228137347190391…48564354960457727999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.392 × 10¹⁰⁰(101-digit number)

13922228137347190391…48564354960457728001

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 #2,160,744

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