Block #632,128

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/14/2014, 12:38:38 AM · Difficulty 10.9627 · 6,162,725 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

86a427ffab93344fd91467cbf2aac0970e0d5518be6ae3b3f6029b1a4b6b740b

View on Chainz ↗

Height

#632,128

Difficulty

10.962729

Transactions

Size

1.41 KB

Version

Bits

0af6756f

Nonce

1,715,097,369

Timestamp

7/14/2014, 12:38:38 AM

Confirmations

6,162,725

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c7a76bb7b95a8d9d0c222fa815e5d59d521aab9190593627065082f5c7afab95

Transactions (4)

Coinbase0d2ea88fe640fa…d02408e2828542

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

db9f202f75974f…5cc9bc6e7c13b2

4 in → 1 out7.3314 XPM637 B

AJAWrWrK…xniax9Ts

d8a1b97cf38145…2a88d731435cac

1 in → 2 out5.1943 XPM227 B

AdvMje6a…b9kFKwGk AUgQ4fAY…TQFhLwZt

b41158c9da1b71…c2c8954dd66154

2 in → 2 out1.0972 XPM374 B

AUfSpLcM…CrXcmDKy ARSrvv1x…ZaaviNgn

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.

1.660 × 10⁹⁷(98-digit number)

16601726962233772407…48666015947605196799

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

1.660 × 10⁹⁷(98-digit number)

16601726962233772407…48666015947605196799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.660 × 10⁹⁷(98-digit number)

16601726962233772407…48666015947605196801

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

3.320 × 10⁹⁷(98-digit number)

33203453924467544814…97332031895210393599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.320 × 10⁹⁷(98-digit number)

33203453924467544814…97332031895210393601

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

6.640 × 10⁹⁷(98-digit number)

66406907848935089628…94664063790420787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.640 × 10⁹⁷(98-digit number)

66406907848935089628…94664063790420787201

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

1.328 × 10⁹⁸(99-digit number)

13281381569787017925…89328127580841574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.328 × 10⁹⁸(99-digit number)

13281381569787017925…89328127580841574401

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

2.656 × 10⁹⁸(99-digit number)

26562763139574035851…78656255161683148799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.656 × 10⁹⁸(99-digit number)

26562763139574035851…78656255161683148801

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