Block #552,457

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/19/2014, 12:06:00 PM · Difficulty 10.9627 · 6,244,401 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99fafd3207ea0c9db9a04fd96b269acdf4ca9a64004b5674d3951aa74be01dad

View on Chainz ↗

Height

#552,457

Difficulty

10.962674

Transactions

Size

1.30 KB

Version

Bits

0af671ce

Nonce

663,194,880

Timestamp

5/19/2014, 12:06:00 PM

Confirmations

6,244,401

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8997e0ef84211bec592de6e698c25bef235dcd0c312ca2ee845ae6195783c675

Transactions (4)

Coinbase329cc70a925306…ff79cf20419ec1

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

ad40db1f3b0740…b9a2b164bcd76d

1 in → 2 out1.6333 XPM226 B

AGdWVjRk…LFVsqCnK ANEPgwhn…6NxoxwM7

abf6f16cb571b4…90fd47075a95fd

2 in → 2 out1.0495 XPM373 B

ASCnrG3m…4bFe7YLG ASPKwH8W…Lxoeu4RM

db1aa1d46b8432…456990bed11c42

3 in → 2 out1.0114 XPM522 B

AVZwze3C…1DNKwKx6 AMJKmGjo…V5agdk4W

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.

1.960 × 10¹⁰⁰(101-digit number)

19608121765122667798…74799909325413529599

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

1.960 × 10¹⁰⁰(101-digit number)

19608121765122667798…74799909325413529599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.960 × 10¹⁰⁰(101-digit number)

19608121765122667798…74799909325413529601

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

3.921 × 10¹⁰⁰(101-digit number)

39216243530245335597…49599818650827059199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.921 × 10¹⁰⁰(101-digit number)

39216243530245335597…49599818650827059201

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

7.843 × 10¹⁰⁰(101-digit number)

78432487060490671195…99199637301654118399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.843 × 10¹⁰⁰(101-digit number)

78432487060490671195…99199637301654118401

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

1.568 × 10¹⁰¹(102-digit number)

15686497412098134239…98399274603308236799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.568 × 10¹⁰¹(102-digit number)

15686497412098134239…98399274603308236801

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

3.137 × 10¹⁰¹(102-digit number)

31372994824196268478…96798549206616473599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.137 × 10¹⁰¹(102-digit number)

31372994824196268478…96798549206616473601

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

6.274 × 10¹⁰¹(102-digit number)

62745989648392536956…93597098413232947199

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