Block #554,319

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/20/2014, 6:34:19 PM · Difficulty 10.9630 · 6,260,715 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

531c11ec23676133ce693479f798eec9a9250cfdabf06fd789c352465b951974

View on Chainz ↗

Height

#554,319

Difficulty

10.963044

Transactions

Size

1.59 KB

Version

Bits

0af68a06

Nonce

2,117,608,617

Timestamp

5/20/2014, 6:34:19 PM

Confirmations

6,260,715

Mined by

⛏️ P2SHAWLL1LQKHiPiM1MxQEWbJGM5oMq3PbiVWN

Merkle Root

a4a31d53cfdeb3acdc77b51e113063d7af4d530245c91350cbe0cbc322325860

Transactions (5)

Coinbased60ea062e70ea5…98e5dc4586e93a

1 in → 1 out8.3500 XPM109 B

AWLL1LQK…q3PbiVWN

89bd7f39ccd906…5883ffe40efef3

1 in → 1 out8.2961 XPM158 B

ALuoRFYG…mxTQxQct

5a8c0d40a25308…0e2274b357635e

1 in → 2 out8.3000 XPM191 B

AHDTi5u9…w5TNUkX7 AeKNrjNj…1NEq95Ta

6d6fdc7a3c2192…ebccd24d257cf5

4 in → 2 out30.1160 XPM672 B

ASG7eNZs…fZJgULA9 AS4dgj1n…wzgUqMbN

c48a5d0ba50994…59732726f54bad

2 in → 3 out7.2416 XPM410 B

AWkTY9wW…HrBW1npq AeKNrjNj…1NEq95Ta AZa2QvH4…JvH9i3cj

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.

3.403 × 10⁹⁵(96-digit number)

34031059381625421033…66988700932745452799

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

3.403 × 10⁹⁵(96-digit number)

34031059381625421033…66988700932745452799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.403 × 10⁹⁵(96-digit number)

34031059381625421033…66988700932745452801

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

6.806 × 10⁹⁵(96-digit number)

68062118763250842067…33977401865490905599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.806 × 10⁹⁵(96-digit number)

68062118763250842067…33977401865490905601

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

1.361 × 10⁹⁶(97-digit number)

13612423752650168413…67954803730981811199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.361 × 10⁹⁶(97-digit number)

13612423752650168413…67954803730981811201

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

2.722 × 10⁹⁶(97-digit number)

27224847505300336827…35909607461963622399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.722 × 10⁹⁶(97-digit number)

27224847505300336827…35909607461963622401

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

5.444 × 10⁹⁶(97-digit number)

54449695010600673654…71819214923927244799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.444 × 10⁹⁶(97-digit number)

54449695010600673654…71819214923927244801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.088 × 10⁹⁷(98-digit number)

10889939002120134730…43638429847854489599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #554,319

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