Block #141,532

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/30/2013, 9:25:55 AM · Difficulty 9.8349 · 6,648,195 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

348b8d10e48badb7b110c75a886a94e72b82263e1efc4458fa0e2f547292ffea

View on Chainz ↗

Height

#141,532

Difficulty

9.834883

Transactions

Size

809 B

Version

Bits

09d5bae0

Nonce

337,900

Timestamp

8/30/2013, 9:25:55 AM

Confirmations

6,648,195

Merkle Root

2b108600dad7f72b3f033064f3a89f5c3f0d34baaabe260988564193afbb4fe7

Transactions (3)

Coinbase9026b6e3fcd9b3…af941761849b8b

1 in → 1 out10.3400 XPM109 B

AL5Ffdxd…zZrTEtCo

1600015a69ba26…48d61ec024cd54

1 in → 2 out272.6500 XPM225 B

AQ2mciw9…v6r6uhvq ANokenZx…sNgASSEm

bc6b019df4959a…a909683b9ab039

3 in → 1 out32.7000 XPM386 B

AX9US9BG…VNQafoJ4

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.

2.546 × 10⁹¹(92-digit number)

25466588755059136103…56859897466299963759

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

2.546 × 10⁹¹(92-digit number)

25466588755059136103…56859897466299963759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.546 × 10⁹¹(92-digit number)

25466588755059136103…56859897466299963761

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

5.093 × 10⁹¹(92-digit number)

50933177510118272206…13719794932599927519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.093 × 10⁹¹(92-digit number)

50933177510118272206…13719794932599927521

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

1.018 × 10⁹²(93-digit number)

10186635502023654441…27439589865199855039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.018 × 10⁹²(93-digit number)

10186635502023654441…27439589865199855041

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

2.037 × 10⁹²(93-digit number)

20373271004047308882…54879179730399710079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.037 × 10⁹²(93-digit number)

20373271004047308882…54879179730399710081

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

4.074 × 10⁹²(93-digit number)

40746542008094617765…09758359460799420159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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