Block #604,669

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/27/2014, 11:22:09 PM · Difficulty 10.9103 · 6,203,249 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ebe5577c4eb1c55815089ab61bc67cd96e15d76028b0d042fe0e49124f6a683

View on Chainz ↗

Height

#604,669

Difficulty

10.910250

Transactions

Size

1.09 KB

Version

Bits

0ae9062a

Nonce

464,469,430

Timestamp

6/27/2014, 11:22:09 PM

Confirmations

6,203,249

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

05cad1959c0baac4d4af6146ea3260389e9d9ff5beb729f6f0e817db9a4f86e9

Transactions (5)

Coinbase0f654bbd0c8d1a…463d7ad85f8e6c

1 in → 1 out8.4300 XPM116 B

ANSXnLY2…Sd25TjkD

699dbb46bb3df8…db61fd78d260c0

1 in → 2 out8.3400 XPM227 B

Aa9TdDYz…3oKRZ7Es ARfmFW1D…yUC4JkJi

694c243d597984…3cd40d9d4664a4

1 in → 2 out2.0210 XPM226 B

AeoQP6Wv…j8wpvrDw ATjwywoV…ga9eRXwi

9ec5388b13a582…6ae3ac76300f3c

1 in → 2 out1.8459 XPM225 B

ASvxN6F7…gzDG9QGb AYz8XXeX…wUExhw54

28cfac7ee42755…0a1eb46ffd453f

1 in → 2 out1.4121 XPM227 B

Ac3gMQ5z…ZjzeaejJ AS9ZCvju…bu3NEFwZ

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.

4.607 × 10⁹⁹(100-digit number)

46073093549385869499…18939757319125155839

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

4.607 × 10⁹⁹(100-digit number)

46073093549385869499…18939757319125155839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.607 × 10⁹⁹(100-digit number)

46073093549385869499…18939757319125155841

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

9.214 × 10⁹⁹(100-digit number)

92146187098771738998…37879514638250311679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.214 × 10⁹⁹(100-digit number)

92146187098771738998…37879514638250311681

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

1.842 × 10¹⁰⁰(101-digit number)

18429237419754347799…75759029276500623359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.842 × 10¹⁰⁰(101-digit number)

18429237419754347799…75759029276500623361

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

3.685 × 10¹⁰⁰(101-digit number)

36858474839508695599…51518058553001246719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.685 × 10¹⁰⁰(101-digit number)

36858474839508695599…51518058553001246721

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

7.371 × 10¹⁰⁰(101-digit number)

73716949679017391198…03036117106002493439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.371 × 10¹⁰⁰(101-digit number)

73716949679017391198…03036117106002493441

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

1.474 × 10¹⁰¹(102-digit number)

14743389935803478239…06072234212004986879

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 #604,669

Cookie Preferences