Block #552,841

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/19/2014, 6:15:45 PM · Difficulty 10.9628 · 6,263,815 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

58380694563da571a2697aa36ebb0366bbadc9c5495446a71c1519b48a093295

View on Chainz ↗

Height

#552,841

Difficulty

10.962785

Transactions

Size

1.26 KB

Version

Bits

0af67919

Nonce

94,875,149

Timestamp

5/19/2014, 6:15:45 PM

Confirmations

6,263,815

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

35f92b29270252c78f2765ac9084cc75b595e2197beea6a7399adc1f06e23a39

Transactions (5)

Coinbase7993d776225a3a…882132320fcdda

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

34a9d6b232c4b1…619dcc5913faf7

2 in → 4 out10.1137 XPM408 B

ARxZwSxP…48ZKixP1 ALG6Kwki…JVRCDqef AeKNrjNj…1NEq95Ta AVAPqikB…BqDErzpV

4095a4bc882684…a4eaa50f7041b8

1 in → 2 out7.7351 XPM226 B

ARpjHv1k…4F9NvuWN ALoDCj2z…wCdCoikq

d0a918380332ad…a1c7892c2e56cf

1 in → 2 out7.2761 XPM226 B

AXiN448S…vbShp5d5 AMEkqRqn…tWAk7KS9

3843efba7a230d…c29f6e8c0d332b

1 in → 2 out3.3197 XPM227 B

AMAxLjXk…843iHH6r AbqqafKd…EpMh3jyG

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.

5.160 × 10⁹⁷(98-digit number)

51605740556288485148…96735321702557698579

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

5.160 × 10⁹⁷(98-digit number)

51605740556288485148…96735321702557698579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.160 × 10⁹⁷(98-digit number)

51605740556288485148…96735321702557698581

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

1.032 × 10⁹⁸(99-digit number)

10321148111257697029…93470643405115397159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.032 × 10⁹⁸(99-digit number)

10321148111257697029…93470643405115397161

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

2.064 × 10⁹⁸(99-digit number)

20642296222515394059…86941286810230794319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.064 × 10⁹⁸(99-digit number)

20642296222515394059…86941286810230794321

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

4.128 × 10⁹⁸(99-digit number)

41284592445030788119…73882573620461588639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.128 × 10⁹⁸(99-digit number)

41284592445030788119…73882573620461588641

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

8.256 × 10⁹⁸(99-digit number)

82569184890061576238…47765147240923177279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.256 × 10⁹⁸(99-digit number)

82569184890061576238…47765147240923177281

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

1.651 × 10⁹⁹(100-digit number)

16513836978012315247…95530294481846354559

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 #552,841

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