Block #151,829

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/5/2013, 10:10:49 PM · Difficulty 9.8620 · 6,661,168 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c52eaf1fc6e4d87a1c003d37a322140eaf11fb88855b003cc0efb0c71217d826

View on Chainz ↗

Height

#151,829

Difficulty

9.862008

Transactions

Size

1.60 KB

Version

Bits

09dcac91

Nonce

94,001

Timestamp

9/5/2013, 10:10:49 PM

Confirmations

6,661,168

Mined by

⛏️ P2SHARbyd1XfYCFbBotLHCWZegP6xUNyieeoWf

Merkle Root

c89e4ea8b9542becff2367e5a890d2228f7f0e7daab424285ad1222cad04d2d6

Transactions (2)

Coinbase526af33a481305…9d112588c42064

1 in → 1 out10.2900 XPM109 B

ARbyd1Xf…NyieeoWf

f0de37087dc71c…65cf450a5edce6

12 in → 2 out123.6000 XPM1.41 KB

AGZvBxxa…shhkwtTn AUYv5H7L…g22JSvJc

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.

6.635 × 10⁹²(93-digit number)

66355380808017870875…71233460827540168319

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

6.635 × 10⁹²(93-digit number)

66355380808017870875…71233460827540168319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.635 × 10⁹²(93-digit number)

66355380808017870875…71233460827540168321

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

1.327 × 10⁹³(94-digit number)

13271076161603574175…42466921655080336639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.327 × 10⁹³(94-digit number)

13271076161603574175…42466921655080336641

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

2.654 × 10⁹³(94-digit number)

26542152323207148350…84933843310160673279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.654 × 10⁹³(94-digit number)

26542152323207148350…84933843310160673281

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

5.308 × 10⁹³(94-digit number)

53084304646414296700…69867686620321346559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.308 × 10⁹³(94-digit number)

53084304646414296700…69867686620321346561

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

1.061 × 10⁹⁴(95-digit number)

10616860929282859340…39735373240642693119

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 #151,829

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