Block #251,529

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 2:03:57 AM · Difficulty 9.9700 · 6,555,934 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7d67d5383d04a0825602ff4506bf1b03f41e7d1dde70580be81ee2dd8bf9b4d

View on Chainz ↗

Height

#251,529

Difficulty

9.969984

Transactions

Size

1.43 KB

Version

Bits

09f850dc

Nonce

27,857

Timestamp

11/9/2013, 2:03:57 AM

Confirmations

6,555,934

Mined by

⛏️ P2SHAVzCheEFNjqKaV9hPMiKg2asJKB8ggQqrh

Merkle Root

a2c16429adc99b58797d868d72e0efb7bfb9a693385456e9b7d4e64f80ab97fb

Transactions (4)

Coinbase84be83b1d8a9e5…a2d6e2f87ad940

1 in → 1 out10.0800 XPM109 B

AVzCheEF…B8ggQqrh

73b7cd59c2f08e…c1bbc28c5ded29

3 in → 2 out129.2935 XPM521 B

AWCD7RLG…99NsfbUA AXEbMG3C…GST83PA5

0a4f83b3203d2f…7b02062d4b28e4

2 in → 2 out10.6168 XPM372 B

ASuoUi24…FwBoFbxd AZzrNvhA…n88CnSqs

186373e543fefc…a72645db29ed4e

2 in → 2 out2.0681 XPM372 B

Af4GuFmE…JnfAUHc6 AdWp2YRv…FDtt217a

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.

2.253 × 10⁹⁷(98-digit number)

22530725541266474798…90082091719490974719

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

2.253 × 10⁹⁷(98-digit number)

22530725541266474798…90082091719490974719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.253 × 10⁹⁷(98-digit number)

22530725541266474798…90082091719490974721

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

4.506 × 10⁹⁷(98-digit number)

45061451082532949597…80164183438981949439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.506 × 10⁹⁷(98-digit number)

45061451082532949597…80164183438981949441

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

9.012 × 10⁹⁷(98-digit number)

90122902165065899194…60328366877963898879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.012 × 10⁹⁷(98-digit number)

90122902165065899194…60328366877963898881

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

1.802 × 10⁹⁸(99-digit number)

18024580433013179838…20656733755927797759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.802 × 10⁹⁸(99-digit number)

18024580433013179838…20656733755927797761

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

3.604 × 10⁹⁸(99-digit number)

36049160866026359677…41313467511855595519

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

Block #251,529

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